Precalculus Examples

$\frac{- 6 x^{3} + 2 x^{2} + 5 x - 10}{x - 2}$

Step 1

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

$2$	$- 6$	$2$	$5$	$- 10$

Step 2

The first number in the dividend $(- 6)$ is put into the first position of the result area (below the horizontal line).

Step 3

Multiply the newest entry in the result $(- 6)$ by the divisor $(2)$ and place the result of $(- 12)$ under the next term in the dividend $(2)$ .

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.

Step 5

Multiply the newest entry in the result $(- 10)$ by the divisor $(2)$ and place the result of $(- 20)$ under the next term in the dividend $(5)$ .

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 $(- 15)$ by the divisor $(2)$ and place the result of $(- 30)$ under the next term in the dividend $(- 10)$ .

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.

$- 6 x^{2} + - 10 x - 15 + \frac{- 40}{x - 2}$

Step 10

Simplify the quotient polynomial.

$- 6 x^{2} - 10 x - 15 - \frac{40}{x - 2}$