Divide Using Long Polynomial Division (-60x^2+8x^4-108)÷(2x-6)

$(- 60 x^{2} + 8 x^{4} - 108) \div (2 x - 6)$

Step 1

Reorder $- 60 x^{2}$ and $8 x^{4}$ .

$\frac{8 x^{4} - 60 x^{2} - 108}{2 x - 6}$

Step 2

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

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

Step 3

Divide the highest order term in the dividend $8 x^{4}$ by the highest order term in divisor $2 x$ .

$4 x^{3}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

Step 4

Multiply the new quotient term by the divisor.

$4 x^{3}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{4} - 24 x^{3}$

$4 x^{3}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

Step 6

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

$4 x^{3}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

Step 7

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

$4 x^{3}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

Step 8

Divide the highest order term in the dividend $24 x^{3}$ by the highest order term in divisor $2 x$ .

$4 x^{3}$

$12 x^{2}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

Step 9

Multiply the new quotient term by the divisor.

$4 x^{3}$

$12 x^{2}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $24 x^{3} - 72 x^{2}$

$4 x^{3}$

$12 x^{2}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

Step 11

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

$4 x^{3}$

$12 x^{2}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

Step 12

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

$4 x^{3}$

$12 x^{2}$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

Step 13

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

$4 x^{3}$

$12 x^{2}$

$6 x$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

Step 14

Multiply the new quotient term by the divisor.

$4 x^{3}$

$12 x^{2}$

$6 x$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{2} - 36 x$

$4 x^{3}$

$12 x^{2}$

$6 x$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

Step 16

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

$4 x^{3}$

$12 x^{2}$

$6 x$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

Step 17

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

$4 x^{3}$

$12 x^{2}$

$6 x$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

$108$

Step 18

Divide the highest order term in the dividend $36 x$ by the highest order term in divisor $2 x$ .

$4 x^{3}$

$12 x^{2}$

$6 x$

$18$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

$108$

Step 19

Multiply the new quotient term by the divisor.

$4 x^{3}$

$12 x^{2}$

$6 x$

$18$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

$108$

$36 x$

$108$

Step 20

The expression needs to be subtracted from the dividend, so change all the signs in $36 x - 108$

$4 x^{3}$

$12 x^{2}$

$6 x$

$18$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

$108$

$36 x$

$108$

Step 21

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

$4 x^{3}$

$12 x^{2}$

$6 x$

$18$

$2 x$

$6$

$8 x^{4}$

$0 x^{3}$

$60 x^{2}$

$0 x$

$108$

$8 x^{4}$

$24 x^{3}$

$60 x^{2}$

$24 x^{3}$

$72 x^{2}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$36 x$

$108$

$36 x$

$108$

$0$

Step 22

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

$4 x^{3} + 12 x^{2} + 6 x + 18$

Divide Using Long Polynomial Division (-60x^2+8x^4-108)÷(2x-6)

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