Divide Using Synthetic Division (4x^3-23x-21)÷(2x+3)

$(4 x^{3} - 23 x - 21) \div (2 x + 3)$

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

$\frac{1}{2} \cdot \frac{4 x^{3} - 23 x - 21}{\frac{2 x + 3}{2}}$

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

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0			\xa0

The first number in the dividend $(4)$ is put into the first position of the result area (below the horizontal line).

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0			\xa0
	$4$

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 $(0)$ .

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$		\xa0
	$4$

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

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$		\xa0
	$4$	$- 6$

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 $(- 23)$ .

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$	$9$	\xa0
	$4$	$- 6$

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

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$	$9$	\xa0
	$4$	$- 6$	$- 14$

Multiply the newest entry in the result $(- 14)$ by the divisor $(- \frac{3}{2})$ and place the result of $(21)$ under the next term in the dividend $(- 21)$ .

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$	$9$	$21$
	$4$	$- 6$	$- 14$

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

$- \frac{3}{2}$	$4$	$0$	$- 23$	$- 21$
	\xa0	$- 6$	$9$	$21$
	$4$	$- 6$	$- 14$	$0$

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

$(\frac{1}{2}) \cdot (4 x^{2} + - 6 x - 14)$

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (4 x^{2} - 6 x - 14)$

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{2} \cdot (4 x^{2} - 6 x) + \frac{1}{2} \cdot - 14$

Apply the distributive property.

$\frac{1}{2} \cdot (4 x^{2}) + \frac{1}{2} \cdot (- 6 x) + \frac{1}{2} \cdot - 14$

Cancel the common factor of $2$ .

Factor $2$ out of $4 x^{2}$ .

$\frac{1}{2} \cdot (2 (2 x^{2})) + \frac{1}{2} \cdot (- 6 x) + \frac{1}{2} \cdot - 14$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (2 x^{2})) + \frac{1}{2} \cdot (- 6 x) + \frac{1}{2} \cdot - 14$

Rewrite the expression.

$2 x^{2} + \frac{1}{2} \cdot (- 6 x) + \frac{1}{2} \cdot - 14$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6 x$ .

$2 x^{2} + \frac{1}{2} \cdot (2 (- 3 x)) + \frac{1}{2} \cdot - 14$

Cancel the common factor.

$2 x^{2} + \frac{1}{2} \cdot (2 (- 3 x)) + \frac{1}{2} \cdot - 14$

Rewrite the expression.

$2 x^{2} - 3 x + \frac{1}{2} \cdot - 14$

Cancel the common factor of $2$ .

Factor $2$ out of $- 14$ .

$2 x^{2} - 3 x + \frac{1}{2} \cdot (2 (- 7))$

Cancel the common factor.

$2 x^{2} - 3 x + \frac{1}{2} \cdot (2 \cdot - 7)$

Rewrite the expression.

$2 x^{2} - 3 x - 7$

Divide Using Synthetic Division (4x^3-23x-21)÷(2x+3)

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