Finite Math Examples

$\frac{(n + 2) (2 n - 1)}{n^{2}}$

Step 1

Expand $(n + 2) (2 n - 1)$ .

Tap for more steps...

Step 1.1

Apply the distributive property.

$\frac{n (2 n - 1) + 2 (2 n - 1)}{n^{2}}$

Step 1.2

Apply the distributive property.

$\frac{n (2 n) + n \cdot - 1 + 2 (2 n - 1)}{n^{2}}$

Step 1.3

Apply the distributive property.

$\frac{n (2 n) + n \cdot - 1 + 2 (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.4

Remove parentheses.

$\frac{n \cdot (2 n) + n \cdot - 1 + 2 (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.5

Reorder $n$ and $2$ .

$\frac{2 \cdot (n \cdot n) + n \cdot - 1 + 2 (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.6

Reorder $n$ and $- 1$ .

$\frac{2 \cdot (n \cdot n) - 1 \cdot n + 2 (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.7

Remove parentheses.

$\frac{2 n \cdot n - 1 n + 2 \cdot (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.8

Raise $n$ to the power of $1$ .

$\frac{2 (n \cdot n) - 1 n + 2 \cdot (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.9

Raise $n$ to the power of $1$ .

$\frac{2 (n \cdot n) - 1 n + 2 \cdot (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.10

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 n^{1 + 1} - 1 n + 2 \cdot (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.11

Add $1$ and $1$ .

$\frac{2 n^{2} - 1 n + 2 \cdot (2 n) + 2 \cdot - 1}{n^{2}}$

Step 1.12

Multiply $2$ by $2$ .

$\frac{2 n^{2} - 1 n + 4 n + 2 \cdot - 1}{n^{2}}$

Step 1.13

Multiply $2$ by $- 1$ .

$\frac{2 n^{2} - 1 n + 4 n - 2}{n^{2}}$

Step 1.14

Add $- 1 n$ and $4 n$ .

$\frac{2 n^{2} + 3 n - 2}{n^{2}}$

Step 2

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

$n^{2}$

$0 n$

$0$

$2 n^{2}$

$3 n$

$2$

Step 3

Divide the highest order term in the dividend $2 n^{2}$ by the highest order term in divisor $n^{2}$ .

							$2$
	$n^{2}$	+	$0 n$	+	$0$		$2 n^{2}$	+	$3 n$	-	$2$

Step 4

Multiply the new quotient term by the divisor.

						$2$
$n^{2}$	+	$0 n$	+	$0$		$2 n^{2}$	+	$3 n$	-	$2$
					+	$2 n^{2}$	+	$0$	+	$0$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $2 n^{2} + 0 + 0$

						$2$
$n^{2}$	+	$0 n$	+	$0$		$2 n^{2}$	+	$3 n$	-	$2$
					-	$2 n^{2}$	-	$0$	-	$0$

Step 6

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

						$2$
$n^{2}$	+	$0 n$	+	$0$		$2 n^{2}$	+	$3 n$	-	$2$
					-	$2 n^{2}$	-	$0$	-	$0$
							+	$3 n$	-	$2$

Step 7

The final answer is the quotient plus the remainder over the divisor.

$2 + \frac{3 n - 2}{n^{2}}$