Divide Using Synthetic Division divide using synthetic division: (6+a^3-a)/(a+2)

divide using synthetic division: $\frac{6 + a^{3} - a}{a + 2}$

Step 1

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

$- 2$	$1$	$0$	$- 1$	$6$
	\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).

Step 3

Multiply the newest entry in the result $(1)$ by the divisor $(- 2)$ and place the result of $(- 2)$ under the next term in the dividend $(0)$ .

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.

Step 5

Multiply the newest entry in the result $(- 2)$ by the divisor $(- 2)$ and place the result of $(4)$ under the next term in the dividend $(- 1)$ .

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.

Step 7

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

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.

Step 9

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

$1 a^{2} + - 2 a + 3$

Step 10

Simplify the quotient polynomial.

$a^{2} - 2 a + 3$