Divide Using Long Polynomial Division (-20x^2+6x^4-16)÷(2x+4)

$(- 20 x^{2} + 6 x^{4} - 16) \div (2 x + 4)$

Step 1

Reorder $- 20 x^{2}$ and $6 x^{4}$ .

$\frac{6 x^{4} - 20 x^{2} - 16}{2 x + 4}$

Step 2

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

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

Step 3

Divide the highest order term in the dividend $6 x^{4}$ by the highest order term in divisor $2 x$ .

$3 x^{3}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

Step 4

Multiply the new quotient term by the divisor.

$3 x^{3}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{4} + 12 x^{3}$

$3 x^{3}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

Step 6

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

$3 x^{3}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

Step 7

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

$3 x^{3}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

Step 8

Divide the highest order term in the dividend $- 12 x^{3}$ by the highest order term in divisor $2 x$ .

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

Step 9

Multiply the new quotient term by the divisor.

				$3 x^{3}$	-	$6 x^{2}$
$2 x$	+	$4$		$6 x^{4}$	+	$0 x^{3}$	-	$20 x^{2}$	+	$0 x$	-	$16$
			-	$6 x^{4}$	-	$12 x^{3}$
					-	$12 x^{3}$	-	$20 x^{2}$
					-	$12 x^{3}$	-	$24 x^{2}$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 12 x^{3} - 24 x^{2}$

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

Step 11

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

Step 12

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

Step 13

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

Step 14

Multiply the new quotient term by the divisor.

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

Step 15

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

Step 16

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

Step 17

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

$16$

Step 18

Divide the highest order term in the dividend $- 8 x$ by the highest order term in divisor $2 x$ .

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

$16$

Step 19

Multiply the new quotient term by the divisor.

				$3 x^{3}$	-	$6 x^{2}$	+	$2 x$	-	$4$
$2 x$	+	$4$		$6 x^{4}$	+	$0 x^{3}$	-	$20 x^{2}$	+	$0 x$	-	$16$
			-	$6 x^{4}$	-	$12 x^{3}$
					-	$12 x^{3}$	-	$20 x^{2}$
					+	$12 x^{3}$	+	$24 x^{2}$
							+	$4 x^{2}$	+	$0 x$
							-	$4 x^{2}$	-	$8 x$
									-	$8 x$	-	$16$
									-	$8 x$	-	$16$

Step 20

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x - 16$

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

$16$

$8 x$

$16$

Step 21

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

$3 x^{3}$

$6 x^{2}$

$2 x$

$4$

$2 x$

$4$

$6 x^{4}$

$0 x^{3}$

$20 x^{2}$

$0 x$

$16$

$6 x^{4}$

$12 x^{3}$

$20 x^{2}$

$12 x^{3}$

$24 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$8 x$

$16$

$8 x$

$16$

$0$

Step 22

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

$3 x^{3} - 6 x^{2} + 2 x - 4$

Divide Using Long Polynomial Division (-20x^2+6x^4-16)÷(2x+4)

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