Calculus Examples

$6 x^{4} - 24 x^{3} - 93 x^{2} + 360 x + 20$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Find the first derivative.

Tap for more steps...

Step 1.1.1

By the Sum Rule, the derivative of $6 x^{4} - 24 x^{3} - 93 x^{2} + 360 x + 20$ with respect to $x$ is $\frac{d}{d x} [6 x^{4}] + \frac{d}{d x} [- 24 x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$ .

$\frac{d}{d x} [6 x^{4}] + \frac{d}{d x} [- 24 x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.2

Evaluate $\frac{d}{d x} [6 x^{4}]$ .

Tap for more steps...

Step 1.1.2.1

Since $6$ is constant with respect to $x$ , the derivative of $6 x^{4}$ with respect to $x$ is $6 \frac{d}{d x} [x^{4}]$ .

$6 \frac{d}{d x} [x^{4}] + \frac{d}{d x} [- 24 x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$6 (4 x^{3}) + \frac{d}{d x} [- 24 x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.2.3

Multiply $4$ by $6$ .

$24 x^{3} + \frac{d}{d x} [- 24 x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.3

Evaluate $\frac{d}{d x} [- 24 x^{3}]$ .

Tap for more steps...

Step 1.1.3.1

Since $- 24$ is constant with respect to $x$ , the derivative of $- 24 x^{3}$ with respect to $x$ is $- 24 \frac{d}{d x} [x^{3}]$ .

$24 x^{3} - 24 \frac{d}{d x} [x^{3}] + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.3.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$24 x^{3} - 24 (3 x^{2}) + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.3.3

Multiply $3$ by $- 24$ .

$24 x^{3} - 72 x^{2} + \frac{d}{d x} [- 93 x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.4

Evaluate $\frac{d}{d x} [- 93 x^{2}]$ .

Tap for more steps...

Step 1.1.4.1

Since $- 93$ is constant with respect to $x$ , the derivative of $- 93 x^{2}$ with respect to $x$ is $- 93 \frac{d}{d x} [x^{2}]$ .

$24 x^{3} - 72 x^{2} - 93 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.4.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$24 x^{3} - 72 x^{2} - 93 (2 x) + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.4.3

Multiply $2$ by $- 93$ .

$24 x^{3} - 72 x^{2} - 186 x + \frac{d}{d x} [360 x] + \frac{d}{d x} [20]$

Step 1.1.5

Evaluate $\frac{d}{d x} [360 x]$ .

Tap for more steps...

Step 1.1.5.1

Since $360$ is constant with respect to $x$ , the derivative of $360 x$ with respect to $x$ is $360 \frac{d}{d x} [x]$ .

$24 x^{3} - 72 x^{2} - 186 x + 360 \frac{d}{d x} [x] + \frac{d}{d x} [20]$

Step 1.1.5.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$24 x^{3} - 72 x^{2} - 186 x + 360 \cdot 1 + \frac{d}{d x} [20]$

Step 1.1.5.3

Multiply $360$ by $1$ .

$24 x^{3} - 72 x^{2} - 186 x + 360 + \frac{d}{d x} [20]$

Step 1.1.6

Differentiate using the Constant Rule.

Tap for more steps...

Step 1.1.6.1

Since $20$ is constant with respect to $x$ , the derivative of $20$ with respect to $x$ is $0$ .

$24 x^{3} - 72 x^{2} - 186 x + 360 + 0$

Step 1.1.6.2

Add $24 x^{3} - 72 x^{2} - 186 x + 360$ and $0$ .

$f' (x) = 24 x^{3} - 72 x^{2} - 186 x + 360$

Step 1.2

The first derivative of $f (x)$ with respect to $x$ is $24 x^{3} - 72 x^{2} - 186 x + 360$ .

$24 x^{3} - 72 x^{2} - 186 x + 360$

Step 2

Set the first derivative equal to $0$ then solve the equation $24 x^{3} - 72 x^{2} - 186 x + 360 = 0$ .

Tap for more steps...

Step 2.1

Set the first derivative equal to $0$ .

$24 x^{3} - 72 x^{2} - 186 x + 360 = 0$

Step 2.2

Factor the left side of the equation.

Tap for more steps...

Step 2.2.1

Factor $6$ out of $24 x^{3} - 72 x^{2} - 186 x + 360$ .

Tap for more steps...

Step 2.2.1.1

Factor $6$ out of $24 x^{3}$ .

$6 (4 x^{3}) - 72 x^{2} - 186 x + 360 = 0$

Step 2.2.1.2

Factor $6$ out of $- 72 x^{2}$ .

$6 (4 x^{3}) + 6 (- 12 x^{2}) - 186 x + 360 = 0$

Step 2.2.1.3

Factor $6$ out of $- 186 x$ .

$6 (4 x^{3}) + 6 (- 12 x^{2}) + 6 (- 31 x) + 360 = 0$

Step 2.2.1.4

Factor $6$ out of $360$ .

$6 (4 x^{3}) + 6 (- 12 x^{2}) + 6 (- 31 x) + 6 (60) = 0$

Step 2.2.1.5

Factor $6$ out of $6 (4 x^{3}) + 6 (- 12 x^{2})$ .

$6 (4 x^{3} - 12 x^{2}) + 6 (- 31 x) + 6 (60) = 0$

Step 2.2.1.6

Factor $6$ out of $6 (4 x^{3} - 12 x^{2}) + 6 (- 31 x)$ .

$6 (4 x^{3} - 12 x^{2} - 31 x) + 6 (60) = 0$

Step 2.2.1.7

Factor $6$ out of $6 (4 x^{3} - 12 x^{2} - 31 x) + 6 (60)$ .

$6 (4 x^{3} - 12 x^{2} - 31 x + 60) = 0$

Step 2.2.2

Factor $4 x^{3} - 12 x^{2} - 31 x + 60$ using the rational roots test.

Tap for more steps...

Step 2.2.2.1

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 60, \pm 2, \pm 30, \pm 3, \pm 20, \pm 4, \pm 15, \pm 5, \pm 12, \pm 6, \pm 10$

$q = \pm 1, \pm 4, \pm 2$

Step 2.2.2.2

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 0.25, \pm 0.5, \pm 60, \pm 15, \pm 30, \pm 2, \pm 7.5, \pm 3, \pm 0.75, \pm 1.5, \pm 20, \pm 5, \pm 10, \pm 4, \pm 3.75, \pm 1.25, \pm 2.5, \pm 12, \pm 6$

Step 2.2.2.3

Substitute $1.5$ and simplify the expression. In this case, the expression is equal to $0$ so $1.5$ is a root of the polynomial.

Tap for more steps...

Step 2.2.2.3.1

Substitute $1.5$ into the polynomial.

$4 \cdot {1.5}^{3} - 12 \cdot {1.5}^{2} - 31 \cdot 1.5 + 60$

Step 2.2.2.3.2

Raise $1.5$ to the power of $3$ .

$4 \cdot 3.375 - 12 \cdot {1.5}^{2} - 31 \cdot 1.5 + 60$

Step 2.2.2.3.3

Multiply $4$ by $3.375$ .

$13.5 - 12 \cdot {1.5}^{2} - 31 \cdot 1.5 + 60$

Step 2.2.2.3.4

Raise $1.5$ to the power of $2$ .

$13.5 - 12 \cdot 2.25 - 31 \cdot 1.5 + 60$

Step 2.2.2.3.5

Multiply $- 12$ by $2.25$ .

$13.5 - 27 - 31 \cdot 1.5 + 60$

Step 2.2.2.3.6

Subtract $27$ from $13.5$ .

$- 13.5 - 31 \cdot 1.5 + 60$

Step 2.2.2.3.7

Multiply $- 31$ by $1.5$ .

$- 13.5 - 46.5 + 60$

Step 2.2.2.3.8

Subtract $46.5$ from $- 13.5$ .

$- 60 + 60$

Step 2.2.2.3.9

Add $- 60$ and $60$ .

$0$

Step 2.2.2.4

Since $1.5$ is a known root, divide the polynomial by $2 x - 3$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$\frac{4 x^{3} - 12 x^{2} - 31 x + 60}{2 x - 3}$

Step 2.2.2.5

Divide $4 x^{3} - 12 x^{2} - 31 x + 60$ by $2 x - 3$ .

Tap for more steps...

Step 2.2.2.5.1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$2 x$

$3$

$4 x^{3}$

$12 x^{2}$

$31 x$

$60$

Step 2.2.2.5.2

Divide the highest order term in the dividend $4 x^{3}$ by the highest order term in divisor $2 x$ .

					$2 x^{2}$
	$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$

Step 2.2.2.5.3

Multiply the new quotient term by the divisor.

				$2 x^{2}$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			+	$4 x^{3}$	-	$6 x^{2}$

Step 2.2.2.5.4

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{3} - 6 x^{2}$

				$2 x^{2}$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$

Step 2.2.2.5.5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$2 x^{2}$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$

Step 2.2.2.5.6

Pull the next terms from the original dividend down into the current dividend.

				$2 x^{2}$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$

Step 2.2.2.5.7

Divide the highest order term in the dividend $- 6 x^{2}$ by the highest order term in divisor $2 x$ .

				$2 x^{2}$	-	$3 x$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$

Step 2.2.2.5.8

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$3 x$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					-	$6 x^{2}$	+	$9 x$

Step 2.2.2.5.9

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 x^{2} + 9 x$

				$2 x^{2}$	-	$3 x$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$

Step 2.2.2.5.10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$2 x^{2}$	-	$3 x$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$

Step 2.2.2.5.11

Pull the next terms from the original dividend down into the current dividend.

				$2 x^{2}$	-	$3 x$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$	+	$60$

Step 2.2.2.5.12

Divide the highest order term in the dividend $- 40 x$ by the highest order term in divisor $2 x$ .

				$2 x^{2}$	-	$3 x$	-	$20$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$	+	$60$

Step 2.2.2.5.13

Multiply the new quotient term by the divisor.

				$2 x^{2}$	-	$3 x$	-	$20$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$	+	$60$
							-	$40 x$	+	$60$

Step 2.2.2.5.14

The expression needs to be subtracted from the dividend, so change all the signs in $- 40 x + 60$

				$2 x^{2}$	-	$3 x$	-	$20$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$	+	$60$
							+	$40 x$	-	$60$

Step 2.2.2.5.15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

				$2 x^{2}$	-	$3 x$	-	$20$
$2 x$	-	$3$		$4 x^{3}$	-	$12 x^{2}$	-	$31 x$	+	$60$
			-	$4 x^{3}$	+	$6 x^{2}$
					-	$6 x^{2}$	-	$31 x$
					+	$6 x^{2}$	-	$9 x$
							-	$40 x$	+	$60$
							+	$40 x$	-	$60$
										$0$

Step 2.2.2.5.16

Since the remander is $0$ , the final answer is the quotient.

$2 x^{2} - 3 x - 20$

Step 2.2.2.6

Write $4 x^{3} - 12 x^{2} - 31 x + 60$ as a set of factors.

$6 ((2 x - 3) (2 x^{2} - 3 x - 20)) = 0$

Step 2.2.3

Factor.

Tap for more steps...

Step 2.2.3.1

Factor by grouping.

Tap for more steps...

Step 2.2.3.1.1

Factor by grouping.

Tap for more steps...

Step 2.2.3.1.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot - 20 = - 40$ and whose sum is $b = - 3$ .

Tap for more steps...

Step 2.2.3.1.1.1.1

Factor $- 3$ out of $- 3 x$ .

$6 ((2 x - 3) (2 x^{2} - 3 x - 20)) = 0$

Step 2.2.3.1.1.1.2

Rewrite $- 3$ as $5$ plus $- 8$

$6 ((2 x - 3) (2 x^{2} + (5 - 8) x - 20)) = 0$

Step 2.2.3.1.1.1.3

Apply the distributive property.

$6 ((2 x - 3) (2 x^{2} + 5 x - 8 x - 20)) = 0$

Step 2.2.3.1.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 2.2.3.1.1.2.1

Group the first two terms and the last two terms.

$6 ((2 x - 3) ((2 x^{2} + 5 x) - 8 x - 20)) = 0$

Step 2.2.3.1.1.2.2

Factor out the greatest common factor (GCF) from each group.

$6 ((2 x - 3) (x (2 x + 5) - 4 (2 x + 5))) = 0$

Step 2.2.3.1.1.3

Factor the polynomial by factoring out the greatest common factor, $2 x + 5$ .

$6 ((2 x - 3) ((2 x + 5) (x - 4))) = 0$

Step 2.2.3.1.2

Remove unnecessary parentheses.

$6 ((2 x - 3) (2 x + 5) (x - 4)) = 0$

Step 2.2.3.2

Remove unnecessary parentheses.

$6 (2 x - 3) (2 x + 5) (x - 4) = 0$

Step 2.3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 3 = 0$

$2 x + 5 = 0$

$x - 4 = 0$

Step 2.4

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Step 2.4.2

Solve $2 x - 3 = 0$ for $x$ .

Tap for more steps...

Step 2.4.2.1

Add $3$ to both sides of the equation.

$2 x = 3$

Step 2.4.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

Tap for more steps...

Step 2.4.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 2.4.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 2.5

Set $2 x + 5$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.5.1

Set $2 x + 5$ equal to $0$ .

$2 x + 5 = 0$

Step 2.5.2

Solve $2 x + 5 = 0$ for $x$ .

Tap for more steps...

Step 2.5.2.1

Subtract $5$ from both sides of the equation.

$2 x = - 5$

Step 2.5.2.2

Divide each term in $2 x = - 5$ by $2$ and simplify.

Tap for more steps...

Step 2.5.2.2.1

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 2.5.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.5.2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.5.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Step 2.5.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Step 2.5.2.2.3

Simplify the right side.

Tap for more steps...

Step 2.5.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

Step 2.6

Set $x - 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.6.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.6.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.7

The final solution is all the values that make $6 (2 x - 3) (2 x + 5) (x - 4) = 0$ true.

$x = \frac{3}{2}, - \frac{5}{2}, 4$

Step 3

Find the values where the derivative is undefined.

Tap for more steps...

Step 3.1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 4

Evaluate $6 x^{4} - 24 x^{3} - 93 x^{2} + 360 x + 20$ at each $x$ value where the derivative is $0$ or undefined.

Tap for more steps...

Step 4.1

Evaluate at $x = \frac{3}{2}$ .

Tap for more steps...

Step 4.1.1

Substitute $\frac{3}{2}$ for $x$ .

$6 {(\frac{3}{2})}^{4} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2

Simplify.

Tap for more steps...

Step 4.1.2.1

Simplify each term.

Tap for more steps...

Step 4.1.2.1.1

Apply the product rule to $\frac{3}{2}$ .

$6 \frac{3^{4}}{2^{4}} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.2

Raise $3$ to the power of $4$ .

$6 \frac{81}{2^{4}} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.3

Raise $2$ to the power of $4$ .

$6 (\frac{81}{16}) - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1.4.1

Factor $2$ out of $6$ .

$2 (3) \frac{81}{16} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.4.2

Factor $2$ out of $16$ .

$2 \cdot 3 \frac{81}{2 \cdot 8} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.4.3

Cancel the common factor.

$2 \cdot 3 \frac{81}{2 \cdot 8} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.4.4

Rewrite the expression.

$3 (\frac{81}{8}) - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.5

Combine $3$ and $\frac{81}{8}$ .

$\frac{3 \cdot 81}{8} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.6

Multiply $3$ by $81$ .

$\frac{243}{8} - 24 {(\frac{3}{2})}^{3} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.7

Apply the product rule to $\frac{3}{2}$ .

$\frac{243}{8} - 24 \frac{3^{3}}{2^{3}} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.8

Raise $3$ to the power of $3$ .

$\frac{243}{8} - 24 \frac{27}{2^{3}} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.9

Raise $2$ to the power of $3$ .

$\frac{243}{8} - 24 (\frac{27}{8}) - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.10

Cancel the common factor of $8$ .

Tap for more steps...

Step 4.1.2.1.10.1

Factor $8$ out of $- 24$ .

$\frac{243}{8} + 8 (- 3) \frac{27}{8} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.10.2

Cancel the common factor.

$\frac{243}{8} + 8 \cdot - 3 \frac{27}{8} - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.10.3

Rewrite the expression.

$\frac{243}{8} - 3 \cdot 27 - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.11

Multiply $- 3$ by $27$ .

$\frac{243}{8} - 81 - 93 {(\frac{3}{2})}^{2} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.12

Apply the product rule to $\frac{3}{2}$ .

$\frac{243}{8} - 81 - 93 \frac{3^{2}}{2^{2}} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.13

Raise $3$ to the power of $2$ .

$\frac{243}{8} - 81 - 93 \frac{9}{2^{2}} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.14

Raise $2$ to the power of $2$ .

$\frac{243}{8} - 81 - 93 (\frac{9}{4}) + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.15

Multiply $- 93 (\frac{9}{4})$ .

Tap for more steps...

Step 4.1.2.1.15.1

Combine $- 93$ and $\frac{9}{4}$ .

$\frac{243}{8} - 81 + \frac{- 93 \cdot 9}{4} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.15.2

Multiply $- 93$ by $9$ .

$\frac{243}{8} - 81 + \frac{- 837}{4} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.16

Move the negative in front of the fraction.

$\frac{243}{8} - 81 - \frac{837}{4} + 360 (\frac{3}{2}) + 20$

Step 4.1.2.1.17

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1.17.1

Factor $2$ out of $360$ .

$\frac{243}{8} - 81 - \frac{837}{4} + 2 (180) \frac{3}{2} + 20$

Step 4.1.2.1.17.2

Cancel the common factor.

$\frac{243}{8} - 81 - \frac{837}{4} + 2 \cdot 180 \frac{3}{2} + 20$

Step 4.1.2.1.17.3

Rewrite the expression.

$\frac{243}{8} - 81 - \frac{837}{4} + 180 \cdot 3 + 20$

Step 4.1.2.1.18

Multiply $180$ by $3$ .

$\frac{243}{8} - 81 - \frac{837}{4} + 540 + 20$

Step 4.1.2.2

Find the common denominator.

Tap for more steps...

Step 4.1.2.2.1

Write $- 81$ as a fraction with denominator $1$ .

$\frac{243}{8} + \frac{- 81}{1} - \frac{837}{4} + 540 + 20$

Step 4.1.2.2.2

Multiply $\frac{- 81}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81}{1} \cdot \frac{8}{8} - \frac{837}{4} + 540 + 20$

Step 4.1.2.2.3

Multiply $\frac{- 81}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837}{4} + 540 + 20$

Step 4.1.2.2.4

Multiply $\frac{837}{4}$ by $\frac{2}{2}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - (\frac{837}{4} \cdot \frac{2}{2}) + 540 + 20$

Step 4.1.2.2.5

Multiply $\frac{837}{4}$ by $\frac{2}{2}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + 540 + 20$

Step 4.1.2.2.6

Write $540$ as a fraction with denominator $1$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540}{1} + 20$

Step 4.1.2.2.7

Multiply $\frac{540}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540}{1} \cdot \frac{8}{8} + 20$

Step 4.1.2.2.8

Multiply $\frac{540}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540 \cdot 8}{8} + 20$

Step 4.1.2.2.9

Write $20$ as a fraction with denominator $1$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540 \cdot 8}{8} + \frac{20}{1}$

Step 4.1.2.2.10

Multiply $\frac{20}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540 \cdot 8}{8} + \frac{20}{1} \cdot \frac{8}{8}$

Step 4.1.2.2.11

Multiply $\frac{20}{1}$ by $\frac{8}{8}$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{4 \cdot 2} + \frac{540 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.1.2.2.12

Reorder the factors of $4 \cdot 2$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{2 \cdot 4} + \frac{540 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.1.2.2.13

Multiply $2$ by $4$ .

$\frac{243}{8} + \frac{- 81 \cdot 8}{8} - \frac{837 \cdot 2}{8} + \frac{540 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.1.2.3

Combine the numerators over the common denominator.

$\frac{243 - 81 \cdot 8 - 837 \cdot 2 + 540 \cdot 8 + 20 \cdot 8}{8}$

Step 4.1.2.4

Simplify each term.

Tap for more steps...

Step 4.1.2.4.1

Multiply $- 81$ by $8$ .

$\frac{243 - 648 - 837 \cdot 2 + 540 \cdot 8 + 20 \cdot 8}{8}$

Step 4.1.2.4.2

Multiply $- 837$ by $2$ .

$\frac{243 - 648 - 1674 + 540 \cdot 8 + 20 \cdot 8}{8}$

Step 4.1.2.4.3

Multiply $540$ by $8$ .

$\frac{243 - 648 - 1674 + 4320 + 20 \cdot 8}{8}$

Step 4.1.2.4.4

Multiply $20$ by $8$ .

$\frac{243 - 648 - 1674 + 4320 + 160}{8}$

Step 4.1.2.5

Simplify by adding and subtracting.

Tap for more steps...

Step 4.1.2.5.1

Subtract $648$ from $243$ .

$\frac{- 405 - 1674 + 4320 + 160}{8}$

Step 4.1.2.5.2

Subtract $1674$ from $- 405$ .

$\frac{- 2079 + 4320 + 160}{8}$

Step 4.1.2.5.3

Add $- 2079$ and $4320$ .

$\frac{2241 + 160}{8}$

Step 4.1.2.5.4

Add $2241$ and $160$ .

$\frac{2401}{8}$

Step 4.2

Evaluate at $x = - \frac{5}{2}$ .

Tap for more steps...

Step 4.2.1

Substitute $- \frac{5}{2}$ for $x$ .

$6 {(- \frac{5}{2})}^{4} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2

Simplify.

Tap for more steps...

Step 4.2.2.1

Simplify each term.

Tap for more steps...

Step 4.2.2.1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 4.2.2.1.1.1

Apply the product rule to $- \frac{5}{2}$ .

$6 ({(- 1)}^{4} {(\frac{5}{2})}^{4}) - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.1.2

Apply the product rule to $\frac{5}{2}$ .

$6 ({(- 1)}^{4} \frac{5^{4}}{2^{4}}) - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.2

Raise $- 1$ to the power of $4$ .

$6 (1 \frac{5^{4}}{2^{4}}) - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.3

Multiply $\frac{5^{4}}{2^{4}}$ by $1$ .

$6 \frac{5^{4}}{2^{4}} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.4

Raise $5$ to the power of $4$ .

$6 \frac{625}{2^{4}} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.5

Raise $2$ to the power of $4$ .

$6 (\frac{625}{16}) - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.6

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.6.1

Factor $2$ out of $6$ .

$2 (3) \frac{625}{16} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.6.2

Factor $2$ out of $16$ .

$2 \cdot 3 \frac{625}{2 \cdot 8} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.6.3

Cancel the common factor.

$2 \cdot 3 \frac{625}{2 \cdot 8} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.6.4

Rewrite the expression.

$3 (\frac{625}{8}) - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.7

Combine $3$ and $\frac{625}{8}$ .

$\frac{3 \cdot 625}{8} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.8

Multiply $3$ by $625$ .

$\frac{1875}{8} - 24 {(- \frac{5}{2})}^{3} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.9

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 4.2.2.1.9.1

Apply the product rule to $- \frac{5}{2}$ .

$\frac{1875}{8} - 24 ({(- 1)}^{3} {(\frac{5}{2})}^{3}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.9.2

Apply the product rule to $\frac{5}{2}$ .

$\frac{1875}{8} - 24 ({(- 1)}^{3} \frac{5^{3}}{2^{3}}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.10

Raise $- 1$ to the power of $3$ .

$\frac{1875}{8} - 24 (- \frac{5^{3}}{2^{3}}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.11

Raise $5$ to the power of $3$ .

$\frac{1875}{8} - 24 (- \frac{125}{2^{3}}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.12

Raise $2$ to the power of $3$ .

$\frac{1875}{8} - 24 (- \frac{125}{8}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.13

Cancel the common factor of $8$ .

Tap for more steps...

Step 4.2.2.1.13.1

Move the leading negative in $- \frac{125}{8}$ into the numerator.

$\frac{1875}{8} - 24 (\frac{- 125}{8}) - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.13.2

Factor $8$ out of $- 24$ .

$\frac{1875}{8} + 8 (- 3) \frac{- 125}{8} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.13.3

Cancel the common factor.

$\frac{1875}{8} + 8 \cdot - 3 \frac{- 125}{8} - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.13.4

Rewrite the expression.

$\frac{1875}{8} - 3 \cdot - 125 - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.14

Multiply $- 3$ by $- 125$ .

$\frac{1875}{8} + 375 - 93 {(- \frac{5}{2})}^{2} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.15

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 4.2.2.1.15.1

Apply the product rule to $- \frac{5}{2}$ .

$\frac{1875}{8} + 375 - 93 ({(- 1)}^{2} {(\frac{5}{2})}^{2}) + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.15.2

Apply the product rule to $\frac{5}{2}$ .

$\frac{1875}{8} + 375 - 93 ({(- 1)}^{2} \frac{5^{2}}{2^{2}}) + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.16

Raise $- 1$ to the power of $2$ .

$\frac{1875}{8} + 375 - 93 (1 \frac{5^{2}}{2^{2}}) + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.17

Multiply $\frac{5^{2}}{2^{2}}$ by $1$ .

$\frac{1875}{8} + 375 - 93 \frac{5^{2}}{2^{2}} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.18

Raise $5$ to the power of $2$ .

$\frac{1875}{8} + 375 - 93 \frac{25}{2^{2}} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.19

Raise $2$ to the power of $2$ .

$\frac{1875}{8} + 375 - 93 (\frac{25}{4}) + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.20

Multiply $- 93 (\frac{25}{4})$ .

Tap for more steps...

Step 4.2.2.1.20.1

Combine $- 93$ and $\frac{25}{4}$ .

$\frac{1875}{8} + 375 + \frac{- 93 \cdot 25}{4} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.20.2

Multiply $- 93$ by $25$ .

$\frac{1875}{8} + 375 + \frac{- 2325}{4} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.21

Move the negative in front of the fraction.

$\frac{1875}{8} + 375 - \frac{2325}{4} + 360 (- \frac{5}{2}) + 20$

Step 4.2.2.1.22

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.22.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{1875}{8} + 375 - \frac{2325}{4} + 360 (\frac{- 5}{2}) + 20$

Step 4.2.2.1.22.2

Factor $2$ out of $360$ .

$\frac{1875}{8} + 375 - \frac{2325}{4} + 2 (180) \frac{- 5}{2} + 20$

Step 4.2.2.1.22.3

Cancel the common factor.

$\frac{1875}{8} + 375 - \frac{2325}{4} + 2 \cdot 180 \frac{- 5}{2} + 20$

Step 4.2.2.1.22.4

Rewrite the expression.

$\frac{1875}{8} + 375 - \frac{2325}{4} + 180 \cdot - 5 + 20$

Step 4.2.2.1.23

Multiply $180$ by $- 5$ .

$\frac{1875}{8} + 375 - \frac{2325}{4} - 900 + 20$

Step 4.2.2.2

Find the common denominator.

Tap for more steps...

Step 4.2.2.2.1

Write $375$ as a fraction with denominator $1$ .

$\frac{1875}{8} + \frac{375}{1} - \frac{2325}{4} - 900 + 20$

Step 4.2.2.2.2

Multiply $\frac{375}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375}{1} \cdot \frac{8}{8} - \frac{2325}{4} - 900 + 20$

Step 4.2.2.2.3

Multiply $\frac{375}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325}{4} - 900 + 20$

Step 4.2.2.2.4

Multiply $\frac{2325}{4}$ by $\frac{2}{2}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - (\frac{2325}{4} \cdot \frac{2}{2}) - 900 + 20$

Step 4.2.2.2.5

Multiply $\frac{2325}{4}$ by $\frac{2}{2}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} - 900 + 20$

Step 4.2.2.2.6

Write $- 900$ as a fraction with denominator $1$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900}{1} + 20$

Step 4.2.2.2.7

Multiply $\frac{- 900}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900}{1} \cdot \frac{8}{8} + 20$

Step 4.2.2.2.8

Multiply $\frac{- 900}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900 \cdot 8}{8} + 20$

Step 4.2.2.2.9

Write $20$ as a fraction with denominator $1$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900 \cdot 8}{8} + \frac{20}{1}$

Step 4.2.2.2.10

Multiply $\frac{20}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900 \cdot 8}{8} + \frac{20}{1} \cdot \frac{8}{8}$

Step 4.2.2.2.11

Multiply $\frac{20}{1}$ by $\frac{8}{8}$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{4 \cdot 2} + \frac{- 900 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.2.2.2.12

Reorder the factors of $4 \cdot 2$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{2 \cdot 4} + \frac{- 900 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.2.2.2.13

Multiply $2$ by $4$ .

$\frac{1875}{8} + \frac{375 \cdot 8}{8} - \frac{2325 \cdot 2}{8} + \frac{- 900 \cdot 8}{8} + \frac{20 \cdot 8}{8}$

Step 4.2.2.3

Combine the numerators over the common denominator.

$\frac{1875 + 375 \cdot 8 - 2325 \cdot 2 - 900 \cdot 8 + 20 \cdot 8}{8}$

Step 4.2.2.4

Simplify each term.

Tap for more steps...

Step 4.2.2.4.1

Multiply $375$ by $8$ .

$\frac{1875 + 3000 - 2325 \cdot 2 - 900 \cdot 8 + 20 \cdot 8}{8}$

Step 4.2.2.4.2

Multiply $- 2325$ by $2$ .

$\frac{1875 + 3000 - 4650 - 900 \cdot 8 + 20 \cdot 8}{8}$

Step 4.2.2.4.3

Multiply $- 900$ by $8$ .

$\frac{1875 + 3000 - 4650 - 7200 + 20 \cdot 8}{8}$

Step 4.2.2.4.4

Multiply $20$ by $8$ .

$\frac{1875 + 3000 - 4650 - 7200 + 160}{8}$

Step 4.2.2.5

Simplify the expression.

Tap for more steps...

Step 4.2.2.5.1

Add $1875$ and $3000$ .

$\frac{4875 - 4650 - 7200 + 160}{8}$

Step 4.2.2.5.2

Subtract $4650$ from $4875$ .

$\frac{225 - 7200 + 160}{8}$

Step 4.2.2.5.3

Subtract $7200$ from $225$ .

$\frac{- 6975 + 160}{8}$

Step 4.2.2.5.4

Add $- 6975$ and $160$ .

$\frac{- 6815}{8}$

Step 4.2.2.5.5

Move the negative in front of the fraction.

$- \frac{6815}{8}$

Step 4.3

Evaluate at $x = 4$ .

Tap for more steps...

Step 4.3.1

Substitute $4$ for $x$ .

$6 {(4)}^{4} - 24 {(4)}^{3} - 93 {(4)}^{2} + 360 (4) + 20$

Step 4.3.2

Simplify.

Tap for more steps...

Step 4.3.2.1

Simplify each term.

Tap for more steps...

Step 4.3.2.1.1

Raise $4$ to the power of $4$ .

$6 \cdot 256 - 24 {(4)}^{3} - 93 {(4)}^{2} + 360 (4) + 20$

Step 4.3.2.1.2

Multiply $6$ by $256$ .

$1536 - 24 {(4)}^{3} - 93 {(4)}^{2} + 360 (4) + 20$

Step 4.3.2.1.3

Raise $4$ to the power of $3$ .

$1536 - 24 \cdot 64 - 93 {(4)}^{2} + 360 (4) + 20$

Step 4.3.2.1.4

Multiply $- 24$ by $64$ .

$1536 - 1536 - 93 {(4)}^{2} + 360 (4) + 20$

Step 4.3.2.1.5

Raise $4$ to the power of $2$ .

$1536 - 1536 - 93 \cdot 16 + 360 (4) + 20$

Step 4.3.2.1.6

Multiply $- 93$ by $16$ .

$1536 - 1536 - 1488 + 360 (4) + 20$

Step 4.3.2.1.7

Multiply $360$ by $4$ .

$1536 - 1536 - 1488 + 1440 + 20$

Step 4.3.2.2

Simplify by adding and subtracting.

Tap for more steps...

Step 4.3.2.2.1

Subtract $1536$ from $1536$ .

$0 - 1488 + 1440 + 20$

Step 4.3.2.2.2

Subtract $1488$ from $0$ .

$- 1488 + 1440 + 20$

Step 4.3.2.2.3

Add $- 1488$ and $1440$ .

$- 48 + 20$

Step 4.3.2.2.4

Add $- 48$ and $20$ .

$- 28$

Step 4.4

List all of the points.

$(\frac{3}{2}, \frac{2401}{8}), (- \frac{5}{2}, - \frac{6815}{8}), (4, - 28)$

Step 5