Precalculus Examples

$\frac{2 x^{3} - 3 x^{2} - 5 x + 4}{x - 2}$

Step 1

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

$2$	$2$	$- 3$	$- 5$	$4$

Step 2

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

Step 3

Multiply the newest entry in the result $(2)$ by the divisor $(2)$ and place the result of $(4)$ under the next term in the dividend $(- 3)$ .

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 $(1)$ by the divisor $(2)$ and place the result of $(2)$ 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 $(- 3)$ by the divisor $(2)$ and place the result of $(- 6)$ under the next term in the dividend $(4)$ .

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.

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

Step 10

Simplify the quotient polynomial.

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