Algebra Examples

$(m^{3} - 12 m^{2} + 33 m) \div (m - 5)$

Step 1

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

$5$	$1$	$- 12$	$33$	$0$

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 $(5)$ and place the result of $(5)$ under the next term in the dividend $(- 12)$ .

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 $(- 7)$ by the divisor $(5)$ and place the result of $(- 35)$ under the next term in the dividend $(33)$ .

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 $(5)$ and place the result of $(- 10)$ under the next term in the dividend $(0)$ .

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.

$1 m^{2} + - 7 m - 2 + \frac{- 10}{m - 5}$

Step 10

Simplify the quotient polynomial.

$m^{2} - 7 m - 2 - \frac{10}{m - 5}$