Pre-Algebra Examples

$(x^{4} + 11 x^{3} + 29 x^{2} - 8 x - 48) \div (x + 4)$

Step 1

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

Step 2

Divide the highest order term in the dividend $x^{4}$ by the highest order term in divisor $x$ .

$x^{3}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

Step 3

Multiply the new quotient term by the divisor.

$x^{3}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $x^{4} + 4 x^{3}$

$x^{3}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

Step 5

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

Step 6

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

Step 7

Divide the highest order term in the dividend $7 x^{3}$ by the highest order term in divisor $x$ .

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

Step 8

Multiply the new quotient term by the divisor.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $7 x^{3} + 28 x^{2}$

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

Step 10

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

Step 11

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

Step 12

Divide the highest order term in the dividend $x^{2}$ by the highest order term in divisor $x$ .

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

Step 13

Multiply the new quotient term by the divisor.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $x^{2} + 4 x$

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

Step 15

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

$12 x$

Step 16

Pull the next terms from the original dividend down into the current dividend.

$x^{3}$

$7 x^{2}$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

$12 x$

$48$

Step 17

Divide the highest order term in the dividend $- 12 x$ by the highest order term in divisor $x$ .

$x^{3}$

$7 x^{2}$

$x$

$12$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

$12 x$

$48$

Step 18

Multiply the new quotient term by the divisor.

				$x^{3}$	+	$7 x^{2}$	+	$x$	-	$12$
$x$	+	$4$		$x^{4}$	+	$11 x^{3}$	+	$29 x^{2}$	-	$8 x$	-	$48$
			-	$x^{4}$	-	$4 x^{3}$
					+	$7 x^{3}$	+	$29 x^{2}$
					-	$7 x^{3}$	-	$28 x^{2}$
							+	$x^{2}$	-	$8 x$
							-	$x^{2}$	-	$4 x$
									-	$12 x$	-	$48$
									-	$12 x$	-	$48$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $- 12 x - 48$

$x^{3}$

$7 x^{2}$

$x$

$12$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

$12 x$

$48$

$12 x$

$48$

Step 20

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$x^{3}$

$7 x^{2}$

$x$

$12$

$x$

$4$

$x^{4}$

$11 x^{3}$

$29 x^{2}$

$8 x$

$48$

$x^{4}$

$4 x^{3}$

$7 x^{3}$

$29 x^{2}$

$7 x^{3}$

$28 x^{2}$

$x^{2}$

$8 x$

$x^{2}$

$4 x$

$12 x$

$48$

$12 x$

$48$

$0$

Step 21

Since the remander is $0$ , the final answer is the quotient.

$x^{3} + 7 x^{2} + x - 12$