Divide Using Synthetic Division (x^7-128)/(x-2)

$\frac{x^{7} - 128}{x - 2}$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0							\xa0

The first number in the dividend $(1)$ is put into the first position of the result area (below the horizontal line).

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0							\xa0
	$1$

Multiply the newest entry in the result $(1)$ by the divisor $(2)$ and place the result of $(2)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$						\xa0
	$1$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$						\xa0
	$1$	$2$

Multiply the newest entry in the result $(2)$ by the divisor $(2)$ and place the result of $(4)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$					\xa0
	$1$	$2$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$					\xa0
	$1$	$2$	$4$

Multiply the newest entry in the result $(4)$ by the divisor $(2)$ and place the result of $(8)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$				\xa0
	$1$	$2$	$4$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$				\xa0
	$1$	$2$	$4$	$8$

Multiply the newest entry in the result $(8)$ by the divisor $(2)$ and place the result of $(16)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$			\xa0
	$1$	$2$	$4$	$8$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$			\xa0
	$1$	$2$	$4$	$8$	$16$

Multiply the newest entry in the result $(16)$ by the divisor $(2)$ and place the result of $(32)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$		\xa0
	$1$	$2$	$4$	$8$	$16$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$		\xa0
	$1$	$2$	$4$	$8$	$16$	$32$

Multiply the newest entry in the result $(32)$ by the divisor $(2)$ and place the result of $(64)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$	$64$	\xa0
	$1$	$2$	$4$	$8$	$16$	$32$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$	$64$	\xa0
	$1$	$2$	$4$	$8$	$16$	$32$	$64$

Multiply the newest entry in the result $(64)$ by the divisor $(2)$ and place the result of $(128)$ under the next term in the dividend $(- 128)$ .

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$	$64$	$128$
	$1$	$2$	$4$	$8$	$16$	$32$	$64$

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

$2$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$- 128$
	\xa0	$2$	$4$	$8$	$16$	$32$	$64$	$128$
	$1$	$2$	$4$	$8$	$16$	$32$	$64$	$0$

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

$1 x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64$

Simplify the quotient polynomial.

$x^{6} + 2 x^{5} + 4 x^{4} + 8 x^{3} + 16 x^{2} + 32 x + 64$

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