Divide Using Synthetic Division (2x^2-17x-38)÷(2x+3)

$(2 x^{2} - 17 x - 38) \div (2 x + 3)$

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

$\frac{1}{2} \cdot \frac{2 x^{2} - 17 x - 38}{\frac{2 x + 3}{2}}$

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

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0		\xa0

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0		\xa0
	$2$

Multiply the newest entry in the result $(2)$ by the divisor $(- \frac{3}{2})$ and place the result of $(- 3)$ under the next term in the dividend $(- 17)$ .

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0	$- 3$	\xa0
	$2$

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

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0	$- 3$	\xa0
	$2$	$- 20$

Multiply the newest entry in the result $(- 20)$ by the divisor $(- \frac{3}{2})$ and place the result of $(30)$ under the next term in the dividend $(- 38)$ .

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0	$- 3$	$30$
	$2$	$- 20$

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

$- \frac{3}{2}$	$2$	$- 17$	$- 38$
	\xa0	$- 3$	$30$
	$2$	$- 20$	$- 8$

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

$(\frac{1}{2}) \cdot ((2) x - 20 + \frac{- 8}{\frac{2 x + 3}{2}})$

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (2 x - 20 - \frac{16}{2 x + 3})$

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{2} \cdot (2 x - 20) + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Apply the distributive property.

$\frac{1}{2} \cdot (2 x) + \frac{1}{2} \cdot - 20 + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} \cdot (2 (x)) + \frac{1}{2} \cdot - 20 + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Cancel the common factor.

$\frac{1}{2} \cdot (2 x) + \frac{1}{2} \cdot - 20 + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Rewrite the expression.

$x + \frac{1}{2} \cdot - 20 + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 20$ .

$x + \frac{1}{2} \cdot (2 (- 10)) + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Cancel the common factor.

$x + \frac{1}{2} \cdot (2 \cdot - 10) + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Rewrite the expression.

$x - 10 + \frac{1}{2} \cdot (- \frac{16}{2 x + 3})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{16}{2 x + 3}$ into the numerator.

$x - 10 + \frac{1}{2} \cdot \frac{- 16}{2 x + 3}$

Factor $2$ out of $- 16$ .

$x - 10 + \frac{1}{2} \cdot \frac{2 (- 8)}{2 x + 3}$

Cancel the common factor.

$x - 10 + \frac{1}{2} \cdot \frac{2 \cdot - 8}{2 x + 3}$

Rewrite the expression.

$x - 10 + \frac{- 8}{2 x + 3}$

Move the negative in front of the fraction.

$x - 10 - \frac{8}{2 x + 3}$

Divide Using Synthetic Division (2x^2-17x-38)÷(2x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.