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

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

Step 1

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

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

Step 2

The first number in the dividend $(3)$ is put into the first position of the result area (below the horizontal line).

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

Step 3

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

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

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.

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

Step 5

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

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

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.

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

Step 7

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

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

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.

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

Step 9

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

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

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.

$- 1$	$3$	$0$	$0$	$0$	$1$	$- 1$
	\xa0	$- 3$	$3$	$- 3$	$3$	\xa0
	$3$	$- 3$	$3$	$- 3$	$4$

Step 11

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

$- 1$	$3$	$0$	$0$	$0$	$1$	$- 1$
	\xa0	$- 3$	$3$	$- 3$	$3$	$- 4$
	$3$	$- 3$	$3$	$- 3$	$4$

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.

$- 1$	$3$	$0$	$0$	$0$	$1$	$- 1$
	\xa0	$- 3$	$3$	$- 3$	$3$	$- 4$
	$3$	$- 3$	$3$	$- 3$	$4$	$- 5$

Step 13

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

$3 m^{4} + - 3 m^{3} + 3 m^{2} + - 3 m + 4 + \frac{- 5}{m + 1}$

Step 14

Simplify the quotient polynomial.

$3 m^{4} - 3 m^{3} + 3 m^{2} - 3 m + 4 - \frac{5}{m + 1}$

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