Precalculus Examples

\frac{5 x^{3} + 18 x^{2} + 7 x - 6}{x + 3}

$\frac{5 x^{3} + 18 x^{2} + 7 x - 6}{x + 3}$

Step 1

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

$- 3$ $- 3$	$5$ $5$	$18$ $18$	$7$ $7$	$- 6$ $- 6$

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

(- 3)

$(- 3)$ and place the result of

(- 15)

$(- 15)$ under the next term in the dividend

(18)

$(18)$ .

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)

$(3)$ by the divisor

(- 3)

$(- 3)$ and place the result of

(- 9)

$(- 9)$ under the next term in the dividend

(7)

$(7)$ .

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)

$(- 2)$ by the divisor

(- 3)

$(- 3)$ and place the result of

(6)

$(6)$ under the next term in the dividend

(- 6)

$(- 6)$ .

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.

5 x^{2} + 3 x - 2

$5 x^{2} + 3 x - 2$