Finite Math Examples

$\frac{9 x^{3} - 10 x + 21}{3 x - 4}$

Step 1

Divide each term in the denominator by $3$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{3} \cdot \frac{9 x^{3} - 10 x + 21}{\frac{3 x - 4}{3}}$

Step 2

Place the numbers representing the divisor and the dividend into a division-like configuration.

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$

Step 3

The first number in the dividend $(9)$ is put into the first position of the result area (below the horizontal line).

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$

	$9$

Step 4

Multiply the newest entry in the result $(9)$ by the divisor $(\frac{4}{3})$ and place the result of $(12)$ under the next term in the dividend $(0)$ .

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$
	$9$

Step 5

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$
	$9$	$12$

Step 6

Multiply the newest entry in the result $(12)$ by the divisor $(\frac{4}{3})$ and place the result of $(16)$ under the next term in the dividend $(- 10)$ .

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$	$16$
	$9$	$12$

Step 7

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$	$16$
	$9$	$12$	$6$

Step 8

Multiply the newest entry in the result $(6)$ by the divisor $(\frac{4}{3})$ and place the result of $(8)$ under the next term in the dividend $(21)$ .

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$	$16$	$8$
	$9$	$12$	$6$

Step 9

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{4}{3}$	$9$	$0$	$- 10$	$21$
		$12$	$16$	$8$
	$9$	$12$	$6$	$29$

Step 10

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$(\frac{1}{3}) \cdot (9 x^{2} + 12 x + 6 + \frac{29}{\frac{3 x - 4}{3}})$

Step 11

Simplify the quotient polynomial.

$(\frac{1}{3}) \cdot (9 x^{2} + 12 x + 6 + \frac{87}{3 x - 4})$

Step 12

Simplify.

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Step 12.1

Distribute.

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Step 12.1.1

Apply the distributive property.

$\frac{1}{3} \cdot (9 x^{2} + 12 x + 6) + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.1.2

Apply the distributive property.

$\frac{1}{3} \cdot (9 x^{2} + 12 x) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.1.3

Apply the distributive property.

$\frac{1}{3} \cdot (9 x^{2}) + \frac{1}{3} \cdot (12 x) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.2

Cancel the common factor of $3$ .

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Step 12.2.1

Factor $3$ out of $9 x^{2}$ .

$\frac{1}{3} \cdot (3 (3 x^{2})) + \frac{1}{3} \cdot (12 x) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 (3 x^{2})) + \frac{1}{3} \cdot (12 x) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.2.3

Rewrite the expression.

$3 x^{2} + \frac{1}{3} \cdot (12 x) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.3

Cancel the common factor of $3$ .

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Step 12.3.1

Factor $3$ out of $12 x$ .

$3 x^{2} + \frac{1}{3} \cdot (3 (4 x)) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.3.2

Cancel the common factor.

$3 x^{2} + \frac{1}{3} \cdot (3 (4 x)) + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.3.3

Rewrite the expression.

$3 x^{2} + 4 x + \frac{1}{3} \cdot 6 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.4

Cancel the common factor of $3$ .

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Step 12.4.1

Factor $3$ out of $6$ .

$3 x^{2} + 4 x + \frac{1}{3} \cdot (3 (2)) + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.4.2

Cancel the common factor.

$3 x^{2} + 4 x + \frac{1}{3} \cdot (3 \cdot 2) + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.4.3

Rewrite the expression.

$3 x^{2} + 4 x + 2 + \frac{1}{3} \cdot \frac{87}{3 x - 4}$

Step 12.5

Cancel the common factor of $3$ .

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Step 12.5.1

Factor $3$ out of $87$ .

$3 x^{2} + 4 x + 2 + \frac{1}{3} \cdot \frac{3 (29)}{3 x - 4}$

Step 12.5.2

Cancel the common factor.

$3 x^{2} + 4 x + 2 + \frac{1}{3} \cdot \frac{3 \cdot 29}{3 x - 4}$

Step 12.5.3

Rewrite the expression.

$3 x^{2} + 4 x + 2 + \frac{29}{3 x - 4}$