Pre-Algebra Examples

$\frac{- 8 x^{3} + 24 x - 42 x + 16}{4 x - 2}$

Step 1

Subtract $42 x$ from $24 x$ .

$\frac{- 8 x^{3} - 18 x + 16}{4 x - 2}$

Step 2

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

$4 x$

$2$

$8 x^{3}$

$0 x^{2}$

$18 x$

$16$

Step 3

Divide the highest order term in the dividend $- 8 x^{3}$ by the highest order term in divisor $4 x$ .

				-	$2 x^{2}$
	$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$

Step 4

Multiply the new quotient term by the divisor.

			-	$2 x^{2}$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			-	$8 x^{3}$	+	$4 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x^{3} + 4 x^{2}$

			-	$2 x^{2}$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$

Step 6

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

			-	$2 x^{2}$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$

Step 7

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

			-	$2 x^{2}$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$

Step 8

Divide the highest order term in the dividend $- 4 x^{2}$ by the highest order term in divisor $4 x$ .

			-	$2 x^{2}$	-	$x$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$

Step 9

Multiply the new quotient term by the divisor.

			-	$2 x^{2}$	-	$x$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					-	$4 x^{2}$	+	$2 x$

Step 10

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

			-	$2 x^{2}$	-	$x$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$

Step 11

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

			-	$2 x^{2}$	-	$x$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$

Step 12

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

			-	$2 x^{2}$	-	$x$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$	+	$16$

Step 13

Divide the highest order term in the dividend $- 20 x$ by the highest order term in divisor $4 x$ .

			-	$2 x^{2}$	-	$x$	-	$5$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$	+	$16$

Step 14

Multiply the new quotient term by the divisor.

			-	$2 x^{2}$	-	$x$	-	$5$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$	+	$16$
							-	$20 x$	+	$10$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $- 20 x + 10$

			-	$2 x^{2}$	-	$x$	-	$5$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$	+	$16$
							+	$20 x$	-	$10$

Step 16

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

			-	$2 x^{2}$	-	$x$	-	$5$
$4 x$	-	$2$	-	$8 x^{3}$	+	$0 x^{2}$	-	$18 x$	+	$16$
			+	$8 x^{3}$	-	$4 x^{2}$
					-	$4 x^{2}$	-	$18 x$
					+	$4 x^{2}$	-	$2 x$
							-	$20 x$	+	$16$
							+	$20 x$	-	$10$
									+	$6$

Step 17

The final answer is the quotient plus the remainder over the divisor.

$- 2 x^{2} - x - 5 + \frac{6}{4 x - 2}$