Divide Using Synthetic Division (x^5+243)/(x+3)

$\frac{(x^{5} + 243)}{(x + 3)}$

Step 1

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

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\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).

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\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 $(0)$ .

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\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.

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\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 $(0)$ .

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\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.

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$			\xa0
	$1$	$- 3$	$9$

Step 7

Multiply the newest entry in the result $(9)$ by the divisor $(- 3)$ and place the result of $(- 27)$ under the next term in the dividend $(0)$ .

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$		\xa0
	$1$	$- 3$	$9$

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.

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$		\xa0
	$1$	$- 3$	$9$	$- 27$

Step 9

Multiply the newest entry in the result $(- 27)$ by the divisor $(- 3)$ and place the result of $(81)$ under the next term in the dividend $(0)$ .

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$	$81$	\xa0
	$1$	$- 3$	$9$	$- 27$

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.

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$	$81$	\xa0
	$1$	$- 3$	$9$	$- 27$	$81$

Step 11

Multiply the newest entry in the result $(81)$ by the divisor $(- 3)$ and place the result of $(- 243)$ under the next term in the dividend $(243)$ .

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$	$81$	$- 243$
	$1$	$- 3$	$9$	$- 27$	$81$

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.

$- 3$	$1$	$0$	$0$	$0$	$0$	$243$
	\xa0	$- 3$	$9$	$- 27$	$81$	$- 243$
	$1$	$- 3$	$9$	$- 27$	$81$	$0$

Step 13

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

$1 x^{4} + - 3 x^{3} + 9 x^{2} + - 27 x + 81$

Step 14

Simplify the quotient polynomial.

$x^{4} - 3 x^{3} + 9 x^{2} - 27 x + 81$

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