Precalculus Examples

$\frac{3 x^{3} + 15 x^{2} + 17 x + 3}{x + 5}$

Step 1

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

$- 5$	$3$	$15$	$17$	$3$

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 $(- 5)$ and place the result of $(- 15)$ under the next term in the dividend $(15)$ .

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 $(0)$ by the divisor $(- 5)$ and place the result of $(0)$ under the next term in the dividend $(17)$ .

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 $(17)$ by the divisor $(- 5)$ and place the result of $(- 85)$ under the next term in the dividend $(3)$ .

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.

Step 9

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

$3 x^{2} + 0 x + 17 + \frac{- 82}{x + 5}$

Step 10

Simplify the quotient polynomial.

$3 x^{2} + 17 - \frac{82}{x + 5}$