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

$\frac{x^{5} + x^{3} - 5}{x - 2}$

Step 1

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

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0					\xa0

Step 2

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

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0					\xa0
	$1$

Step 3

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 $(0)$ .

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$				\xa0
	$1$

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.

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$				\xa0
	$1$	$2$

Step 5

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 $(1)$ .

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$			\xa0
	$1$	$2$

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.

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$			\xa0
	$1$	$2$	$5$

Step 7

Multiply the newest entry in the result $(5)$ by the divisor $(2)$ and place the result of $(10)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$		\xa0
	$1$	$2$	$5$

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.

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$		\xa0
	$1$	$2$	$5$	$10$

Step 9

Multiply the newest entry in the result $(10)$ by the divisor $(2)$ and place the result of $(20)$ under the next term in the dividend $(0)$ .

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$	$20$	\xa0
	$1$	$2$	$5$	$10$

Step 10

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

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$	$20$	\xa0
	$1$	$2$	$5$	$10$	$20$

Step 11

Multiply the newest entry in the result $(20)$ by the divisor $(2)$ and place the result of $(40)$ under the next term in the dividend $(- 5)$ .

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$	$20$	$40$
	$1$	$2$	$5$	$10$	$20$

Step 12

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

$2$	$1$	$0$	$1$	$0$	$0$	$- 5$
	\xa0	$2$	$4$	$10$	$20$	$40$
	$1$	$2$	$5$	$10$	$20$	$35$

Step 13

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

$1 x^{4} + 2 x^{3} + 5 x^{2} + 10 x + 20 + \frac{35}{x - 2}$

Step 14

Simplify the quotient polynomial.

$x^{4} + 2 x^{3} + 5 x^{2} + 10 x + 20 + \frac{35}{x - 2}$

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