Precalculus Examples

(5 x^{3} + 21 x^{2} - 16) \div (x + 4)

$(5 x^{3} + 21 x^{2} - 16) \div (x + 4)$

Step 1

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

$- 4$ $- 4$	$5$ $5$	$21$ $21$	$0$ $0$	$- 16$ $- 16$

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

(- 4)

$(- 4)$ and place the result of

(- 20)

$(- 20)$ under the next term in the dividend

(21)

$(21)$ .

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)

$(1)$ by the divisor

(- 4)

$(- 4)$ and place the result of

(- 4)

$(- 4)$ under the next term in the dividend

(0)

$(0)$ .

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

(- 4)

$(- 4)$ by the divisor

(- 4)

$(- 4)$ and place the result of

(16)

$(16)$ under the next term in the dividend

(- 16)

$(- 16)$ .

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} + 1 x - 4

$5 x^{2} + 1 x - 4$

Step 10

Simplify the quotient polynomial.

5 x^{2} + x - 4

$5 x^{2} + x - 4$

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