Divide Using Synthetic Division (40x^3+4x^2-6)÷(2x+1)

$(40 x^{3} + 4 x^{2} - 6) \div (2 x + 1)$

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

$\frac{1}{2} \cdot \frac{40 x^{3} + 4 x^{2} - 6}{\frac{2 x + 1}{2}}$

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

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0			\xa0

The first number in the dividend $(40)$ is put into the first position of the result area (below the horizontal line).

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0			\xa0
	$40$

Multiply the newest entry in the result $(40)$ by the divisor $(- \frac{1}{2})$ and place the result of $(- 20)$ under the next term in the dividend $(4)$ .

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$		\xa0
	$40$

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

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$		\xa0
	$40$	$- 16$

Multiply the newest entry in the result $(- 16)$ by the divisor $(- \frac{1}{2})$ and place the result of $(8)$ under the next term in the dividend $(0)$ .

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$	$8$	\xa0
	$40$	$- 16$

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

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$	$8$	\xa0
	$40$	$- 16$	$8$

Multiply the newest entry in the result $(8)$ by the divisor $(- \frac{1}{2})$ and place the result of $(- 4)$ under the next term in the dividend $(- 6)$ .

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$	$8$	$- 4$
	$40$	$- 16$	$8$

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

$- \frac{1}{2}$	$40$	$4$	$0$	$- 6$
	\xa0	$- 20$	$8$	$- 4$
	$40$	$- 16$	$8$	$- 10$

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

$(\frac{1}{2}) \cdot (40 x^{2} + - 16 x + 8 + \frac{- 10}{\frac{2 x + 1}{2}})$

Simplify the quotient polynomial.

$(\frac{1}{2}) \cdot (40 x^{2} - 16 x + 8 - \frac{20}{2 x + 1})$

Simplify.

Distribute.

Apply the distributive property.

$\frac{1}{2} \cdot (40 x^{2} - 16 x + 8) + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Apply the distributive property.

$\frac{1}{2} \cdot (40 x^{2} - 16 x) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Apply the distributive property.

$\frac{1}{2} \cdot (40 x^{2}) + \frac{1}{2} \cdot (- 16 x) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Cancel the common factor of $2$ .

Factor $2$ out of $40 x^{2}$ .

$\frac{1}{2} \cdot (2 (20 x^{2})) + \frac{1}{2} \cdot (- 16 x) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (20 x^{2})) + \frac{1}{2} \cdot (- 16 x) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Rewrite the expression.

$20 x^{2} + \frac{1}{2} \cdot (- 16 x) + \frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 16 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$20 x^{2} - 8 x + \frac{1}{2} \cdot (2 (4)) + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Cancel the common factor.

$20 x^{2} - 8 x + \frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Rewrite the expression.

$20 x^{2} - 8 x + 4 + \frac{1}{2} \cdot (- \frac{20}{2 x + 1})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{20}{2 x + 1}$ into the numerator.

$20 x^{2} - 8 x + 4 + \frac{1}{2} \cdot \frac{- 20}{2 x + 1}$

Factor $2$ out of $- 20$ .

$20 x^{2} - 8 x + 4 + \frac{1}{2} \cdot \frac{2 (- 10)}{2 x + 1}$

Cancel the common factor.

$20 x^{2} - 8 x + 4 + \frac{1}{2} \cdot \frac{2 \cdot - 10}{2 x + 1}$

Rewrite the expression.

$20 x^{2} - 8 x + 4 + \frac{- 10}{2 x + 1}$

Move the negative in front of the fraction.

$20 x^{2} - 8 x + 4 - \frac{10}{2 x + 1}$

Divide Using Synthetic Division (40x^3+4x^2-6)÷(2x+1)

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