Divide Using Synthetic Division (9x^4-3x^3-20x^2+24x+32)÷(3x+4)

$(9 x^{4} - 3 x^{3} - 20 x^{2} + 24 x + 32) \div (3 x + 4)$

Step 1

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

$\frac{1}{3} \cdot \frac{9 x^{4} - 3 x^{3} - 20 x^{2} + 24 x + 32}{\frac{3 x + 4}{3}}$

Step 2

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

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0				\xa0

Step 3

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

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0				\xa0
	$9$

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 $(- 3)$ .

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$			\xa0
	$9$

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.

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$			\xa0
	$9$	$- 15$

Step 6

Multiply the newest entry in the result $(- 15)$ by the divisor $(- \frac{4}{3})$ and place the result of $(20)$ under the next term in the dividend $(- 20)$ .

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$		\xa0
	$9$	$- 15$

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.

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$		\xa0
	$9$	$- 15$	$0$

Step 8

Multiply the newest entry in the result $(0)$ by the divisor $(- \frac{4}{3})$ and place the result of $(0)$ under the next term in the dividend $(24)$ .

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$	$0$	\xa0
	$9$	$- 15$	$0$

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.

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$	$0$	\xa0
	$9$	$- 15$	$0$	$24$

Step 10

Multiply the newest entry in the result $(24)$ by the divisor $(- \frac{4}{3})$ and place the result of $(- 32)$ under the next term in the dividend $(32)$ .

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$	$0$	$- 32$
	$9$	$- 15$	$0$	$24$

Step 11

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

$- \frac{4}{3}$	$9$	$- 3$	$- 20$	$24$	$32$
	\xa0	$- 12$	$20$	$0$	$- 32$
	$9$	$- 15$	$0$	$24$	$0$

Step 12

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

$(\frac{1}{3}) \cdot (9 x^{3} + - 15 x^{2} + (0) x + 24)$

Step 13

Simplify the quotient polynomial.

$(\frac{1}{3}) \cdot (9 x^{3} - 15 x^{2} + 24)$

Step 14

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{3} \cdot (9 x^{3} - 15 x^{2}) + \frac{1}{3} \cdot 24$

Apply the distributive property.

$\frac{1}{3} \cdot (9 x^{3}) + \frac{1}{3} \cdot (- 15 x^{2}) + \frac{1}{3} \cdot 24$

Cancel the common factor of $3$ .

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

$\frac{1}{3} \cdot (3 (3 x^{3})) + \frac{1}{3} \cdot (- 15 x^{2}) + \frac{1}{3} \cdot 24$

Cancel the common factor.

$\frac{1}{3} \cdot (3 (3 x^{3})) + \frac{1}{3} \cdot (- 15 x^{2}) + \frac{1}{3} \cdot 24$

Rewrite the expression.

$3 x^{3} + \frac{1}{3} \cdot (- 15 x^{2}) + \frac{1}{3} \cdot 24$

Cancel the common factor of $3$ .

Factor $3$ out of $- 15 x^{2}$ .

$3 x^{3} + \frac{1}{3} \cdot (3 (- 5 x^{2})) + \frac{1}{3} \cdot 24$

Cancel the common factor.

$3 x^{3} + \frac{1}{3} \cdot (3 (- 5 x^{2})) + \frac{1}{3} \cdot 24$

Rewrite the expression.

$3 x^{3} - 5 x^{2} + \frac{1}{3} \cdot 24$

Cancel the common factor of $3$ .

Factor $3$ out of $24$ .

$3 x^{3} - 5 x^{2} + \frac{1}{3} \cdot (3 (8))$

Cancel the common factor.

$3 x^{3} - 5 x^{2} + \frac{1}{3} \cdot (3 \cdot 8)$

Rewrite the expression.

$3 x^{3} - 5 x^{2} + 8$

Divide Using Synthetic Division (9x^4-3x^3-20x^2+24x+32)÷(3x+4)

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