Precalculus Examples

$\frac{x^{3} - 11 x + 3}{x - 3}$

Step 1

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

$3$	$1$	$0$	$- 11$	$3$

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 $(3)$ and place the result of $(3)$ 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 $(3)$ by the divisor $(3)$ and place the result of $(9)$ under the next term in the dividend $(- 11)$ .

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 $(3)$ and place the result of $(- 6)$ 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.

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

Step 10

Simplify the quotient polynomial.

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