Divide Using Synthetic Division (x^5+x^3-1)/(x-4)

$\frac{x^{5} + x^{3} - 1}{x - 4}$

Step 1

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

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\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).

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0					\xa0
	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(4)$ and place the result of $(4)$ under the next term in the dividend $(0)$ .

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$				\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.

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$				\xa0
	$1$	$4$

Step 5

Multiply the newest entry in the result $(4)$ by the divisor $(4)$ and place the result of $(16)$ under the next term in the dividend $(1)$ .

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$			\xa0
	$1$	$4$

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.

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$			\xa0
	$1$	$4$	$17$

Step 7

Multiply the newest entry in the result $(17)$ by the divisor $(4)$ and place the result of $(68)$ under the next term in the dividend $(0)$ .

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$		\xa0
	$1$	$4$	$17$

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.

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$		\xa0
	$1$	$4$	$17$	$68$

Step 9

Multiply the newest entry in the result $(68)$ by the divisor $(4)$ and place the result of $(272)$ under the next term in the dividend $(0)$ .

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$	$272$	\xa0
	$1$	$4$	$17$	$68$

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.

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$	$272$	\xa0
	$1$	$4$	$17$	$68$	$272$

Step 11

Multiply the newest entry in the result $(272)$ by the divisor $(4)$ and place the result of $(1088)$ under the next term in the dividend $(- 1)$ .

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$	$272$	$1088$
	$1$	$4$	$17$	$68$	$272$

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.

$4$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$4$	$16$	$68$	$272$	$1088$
	$1$	$4$	$17$	$68$	$272$	$1087$

Step 13

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

$1 x^{4} + 4 x^{3} + 17 x^{2} + 68 x + 272 + \frac{1087}{x - 4}$

Step 14

Simplify the quotient polynomial.

$x^{4} + 4 x^{3} + 17 x^{2} + 68 x + 272 + \frac{1087}{x - 4}$

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