Precalculus Examples

$\frac{5 x^{3} + 6 x + 8}{x + 2}$

Step 1

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

$- 2$	$5$	$0$	$6$	$8$

Step 2

The first number in the dividend $(5)$ is put into the first position of the result area (below the horizontal line).

Step 3

Multiply the newest entry in the result $(5)$ by the divisor $(- 2)$ and place the result of $(- 10)$ 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 $(- 10)$ by the divisor $(- 2)$ and place the result of $(20)$ under the next term in the dividend $(6)$ .

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.

Step 7

Multiply the newest entry in the result $(26)$ by the divisor $(- 2)$ and place the result of $(- 52)$ under the next term in the dividend $(8)$ .

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.

$5 x^{2} + - 10 x + 26 + \frac{- 44}{x + 2}$

Step 10

Simplify the quotient polynomial.

$5 x^{2} - 10 x + 26 - \frac{44}{x + 2}$