Divide Using Synthetic Division (6x^3+5x^2+9)/(2x+3)

$\frac{6 x^{3} + 5 x^{2} + 9}{2 x + 3}$

Step 1

Divide each term in the denominator by $2$ to make the coefficient of linear factor variable $1$ .

$\frac{1}{2} \cdot \frac{6 x^{3} + 5 x^{2} + 9}{\frac{2 x + 3}{2}}$

Step 2

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

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0			\xa0

Step 3

The first number in the dividend $(6)$ is put into the first position of the result area (below the horizontal line).

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0			\xa0
	$6$

Step 4

Multiply the newest entry in the result $(6)$ by the divisor $(- \frac{3}{2})$ and place the result of $(- 9)$ under the next term in the dividend $(5)$ .

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$		\xa0
	$6$

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.

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$		\xa0
	$6$	$- 4$

Step 6

Multiply the newest entry in the result $(- 4)$ by the divisor $(- \frac{3}{2})$ and place the result of $(6)$ under the next term in the dividend $(0)$ .

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$	$6$	\xa0
	$6$	$- 4$

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.

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$	$6$	\xa0
	$6$	$- 4$	$6$

Step 8

Multiply the newest entry in the result $(6)$ by the divisor $(- \frac{3}{2})$ and place the result of $(- 9)$ under the next term in the dividend $(9)$ .

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$	$6$	$- 9$
	$6$	$- 4$	$6$

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.

$- \frac{3}{2}$	$6$	$5$	$0$	$9$
	\xa0	$- 9$	$6$	$- 9$
	$6$	$- 4$	$6$	$0$

Step 10

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

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

Step 11

Simplify the quotient polynomial.

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

Step 12

Simplify.

Distribute.

Apply the distributive property.

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide Using Synthetic Division (6x^3+5x^2+9)/(2x+3)

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