Divide Using Synthetic Division (3x^3-5x^2-2)÷(x-1)

$(3 x^{3} - 5 x^{2} - 2) \div (x - 1)$

Step 1

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

$1$	$3$	$- 5$	$0$	$- 2$
	\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).

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 $(- 5)$ .

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 $(1)$ and place the result of $(- 2)$ under the next term in the dividend $(0)$ .

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

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.

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

Step 10

Simplify the quotient polynomial.

$3 x^{2} - 2 x - 2 - \frac{4}{x - 1}$