Divide Using Synthetic Division (8x^3+2x^2-5x+1)÷(x-1/2)

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

Step 1

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

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0			\xa0

Step 2

The first number in the dividend $(8)$ is put into the first position of the result area (below the horizontal line).

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0			\xa0
	$8$

Step 3

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 $(2)$ .

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$		\xa0
	$8$

Step 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.

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$		\xa0
	$8$	$6$

Step 5

Multiply the newest entry in the result $(6)$ by the divisor $(\frac{1}{2})$ and place the result of $(3)$ under the next term in the dividend $(- 5)$ .

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$	$3$	\xa0
	$8$	$6$

Step 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.

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$	$3$	\xa0
	$8$	$6$	$- 2$

Step 7

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

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$	$3$	$- 1$
	$8$	$6$	$- 2$

Step 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.

$\frac{1}{2}$	$8$	$2$	$- 5$	$1$
	\xa0	$4$	$3$	$- 1$
	$8$	$6$	$- 2$	$0$

Step 9

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

$8 x^{2} + 6 x - 2$

Divide Using Synthetic Division (8x^3+2x^2-5x+1)÷(x-1/2)

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