Algebra Examples

(x^{4} + 13 x^{3} - 64 x^{2} - 20 x + 16) \div (x - 4)

$(x^{4} + 13 x^{3} - 64 x^{2} - 20 x + 16) \div (x - 4)$

Step 1

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

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$

Step 2

The first number in the dividend

(1)

$(1)$ is put into the first position of the result area (below the horizontal line).

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$

	$1$ $1$

Step 3

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

(13)

$(13)$ .

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$
	$1$ $1$

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.

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$
	$1$ $1$	$17$ $17$

Step 5

Multiply the newest entry in the result

(17)

$(17)$ by the divisor

(4)

$(4)$ and place the result of

(68)

$(68)$ under the next term in the dividend

(- 64)

$(- 64)$ .

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$
	$1$ $1$	$17$ $17$

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.

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$
	$1$ $1$	$17$ $17$	$4$ $4$

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

(- 20)

$(- 20)$ .

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$	$16$ $16$
	$1$ $1$	$17$ $17$	$4$ $4$

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.

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$	$16$ $16$
	$1$ $1$	$17$ $17$	$4$ $4$	$- 4$ $- 4$

Step 9

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)

$(16)$ .

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$	$16$ $16$	$- 16$ $- 16$
	$1$ $1$	$17$ $17$	$4$ $4$	$- 4$ $- 4$

Step 10

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$4$ $4$	$1$ $1$	$13$ $13$	$- 64$ $- 64$	$- 20$ $- 20$	$16$ $16$
		$4$ $4$	$68$ $68$	$16$ $16$	$- 16$ $- 16$
	$1$ $1$	$17$ $17$	$4$ $4$	$- 4$ $- 4$	$0$ $0$

Step 11

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

1 x^{3} + 17 x^{2} + (4) x - 4

$1 x^{3} + 17 x^{2} + (4) x - 4$

Step 12

Simplify the quotient polynomial.

x^{3} + 17 x^{2} + 4 x - 4

$x^{3} + 17 x^{2} + 4 x - 4$