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

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

Step 1

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

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\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).

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0					\xa0
	$1$

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(3)$ and place the result of $(3)$ under the next term in the dividend $(0)$ .

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$				\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.

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$				\xa0
	$1$	$3$

Step 5

Multiply the newest entry in the result $(3)$ by the divisor $(3)$ and place the result of $(9)$ under the next term in the dividend $(1)$ .

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$			\xa0
	$1$	$3$

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.

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$			\xa0
	$1$	$3$	$10$

Step 7

Multiply the newest entry in the result $(10)$ by the divisor $(3)$ and place the result of $(30)$ under the next term in the dividend $(0)$ .

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$		\xa0
	$1$	$3$	$10$

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.

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$		\xa0
	$1$	$3$	$10$	$30$

Step 9

Multiply the newest entry in the result $(30)$ by the divisor $(3)$ and place the result of $(90)$ under the next term in the dividend $(0)$ .

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$	$90$	\xa0
	$1$	$3$	$10$	$30$

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.

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$	$90$	\xa0
	$1$	$3$	$10$	$30$	$90$

Step 11

Multiply the newest entry in the result $(90)$ by the divisor $(3)$ and place the result of $(270)$ under the next term in the dividend $(- 1)$ .

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$	$90$	$270$
	$1$	$3$	$10$	$30$	$90$

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.

$3$	$1$	$0$	$1$	$0$	$0$	$- 1$
	\xa0	$3$	$9$	$30$	$90$	$270$
	$1$	$3$	$10$	$30$	$90$	$269$

Step 13

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

$1 x^{4} + 3 x^{3} + 10 x^{2} + 30 x + 90 + \frac{269}{x - 3}$

Step 14

Simplify the quotient polynomial.

$x^{4} + 3 x^{3} + 10 x^{2} + 30 x + 90 + \frac{269}{x - 3}$

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