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

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

Step 1

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

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0					\xa0

Step 2

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0					\xa0
	$2$

Step 3

Multiply the newest entry in the result $(2)$ by the divisor $(3)$ and place the result of $(6)$ under the next term in the dividend $(0)$ .

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$				\xa0
	$2$

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.

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$				\xa0
	$2$	$6$

Step 5

Multiply the newest entry in the result $(6)$ by the divisor $(3)$ and place the result of $(18)$ under the next term in the dividend $(- 3)$ .

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$			\xa0
	$2$	$6$

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.

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$			\xa0
	$2$	$6$	$15$

Step 7

Multiply the newest entry in the result $(15)$ by the divisor $(3)$ and place the result of $(45)$ under the next term in the dividend $(0)$ .

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$		\xa0
	$2$	$6$	$15$

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.

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$		\xa0
	$2$	$6$	$15$	$45$

Step 9

Multiply the newest entry in the result $(45)$ by the divisor $(3)$ and place the result of $(135)$ under the next term in the dividend $(1)$ .

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$	$135$	\xa0
	$2$	$6$	$15$	$45$

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.

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$	$135$	\xa0
	$2$	$6$	$15$	$45$	$136$

Step 11

Multiply the newest entry in the result $(136)$ by the divisor $(3)$ and place the result of $(408)$ under the next term in the dividend $(0)$ .

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$	$135$	$408$
	$2$	$6$	$15$	$45$	$136$

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.

$3$	$2$	$0$	$- 3$	$0$	$1$	$0$
	\xa0	$6$	$18$	$45$	$135$	$408$
	$2$	$6$	$15$	$45$	$136$	$408$

Step 13

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

$2 x^{4} + 6 x^{3} + 15 x^{2} + 45 x + 136 + \frac{408}{x - 3}$

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