Pre-Algebra Examples

$(- 2 w^{3} - 7 w^{2} - 2 w + 3) \div (w - \frac{1}{2})$

Step 1

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

$w$

$\frac{1}{2}$

$2 w^{3}$

$7 w^{2}$

$2 w$

$3$

Step 2

Divide the highest order term in the dividend $- 2 w^{3}$ by the highest order term in divisor $w$ .

				-	$2 w^{2}$
	$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$

Step 3

Multiply the new quotient term by the divisor.

			-	$2 w^{2}$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			-	$2 w^{3}$	+	$w^{2}$

Step 4

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

			-	$2 w^{2}$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$

Step 5

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

			-	$2 w^{2}$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$

Step 6

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

			-	$2 w^{2}$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$

Step 7

Divide the highest order term in the dividend $- 8 w^{2}$ by the highest order term in divisor $w$ .

			-	$2 w^{2}$	-	$8 w$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$

Step 8

Multiply the new quotient term by the divisor.

			-	$2 w^{2}$	-	$8 w$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					-	$8 w^{2}$	+	$4 w$

Step 9

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

			-	$2 w^{2}$	-	$8 w$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$

Step 10

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

			-	$2 w^{2}$	-	$8 w$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$

Step 11

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

			-	$2 w^{2}$	-	$8 w$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$	+	$3$

Step 12

Divide the highest order term in the dividend $- 6 w$ by the highest order term in divisor $w$ .

			-	$2 w^{2}$	-	$8 w$	-	$6$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$	+	$3$

Step 13

Multiply the new quotient term by the divisor.

			-	$2 w^{2}$	-	$8 w$	-	$6$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$	+	$3$
							-	$6 w$	+	$3$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 w + 3$

			-	$2 w^{2}$	-	$8 w$	-	$6$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$	+	$3$
							+	$6 w$	-	$3$

Step 15

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

			-	$2 w^{2}$	-	$8 w$	-	$6$
$w$	-	$\frac{1}{2}$	-	$2 w^{3}$	-	$7 w^{2}$	-	$2 w$	+	$3$
			+	$2 w^{3}$	-	$w^{2}$
					-	$8 w^{2}$	-	$2 w$
					+	$8 w^{2}$	-	$4 w$
							-	$6 w$	+	$3$
							+	$6 w$	-	$3$
										$0$

Step 16

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

$- 2 w^{2} - 8 w - 6$