Examples

(5 x^{2} + 36 x + 40) \div (x + 6)

$(5 x^{2} + 36 x + 40) \div (x + 6)$

Step 1

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

$- 6$ $- 6$	$5$ $5$	$36$ $36$	$40$ $40$

Step 2

The first number in the dividend

(5)

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

Step 3

Multiply the newest entry in the result

(5)

$(5)$ by the divisor

(- 6)

$(- 6)$ and place the result of

(- 30)

$(- 30)$ under the next term in the dividend

(36)

$(36)$ .

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

(6)

$(6)$ by the divisor

(- 6)

$(- 6)$ and place the result of

(- 36)

$(- 36)$ under the next term in the dividend

(40)

$(40)$ .

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

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

(5) x + 6 + \frac{4}{x + 6}

$(5) x + 6 + \frac{4}{x + 6}$

Step 8

Simplify the quotient polynomial.

5 x + 6 + \frac{4}{x + 6}

$5 x + 6 + \frac{4}{x + 6}$

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