Algebra Examples

$(- 92 x^{2} + 6 x^{4} - 64) \div (2 x - 8)$

Step 1

Reorder $- 92 x^{2}$ and $6 x^{4}$ .

$\frac{6 x^{4} - 92 x^{2} - 64}{2 x - 8}$

Step 2

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

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

Step 3

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

$3 x^{3}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

Step 4

Multiply the new quotient term by the divisor.

$3 x^{3}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $6 x^{4} - 24 x^{3}$

$3 x^{3}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

Step 6

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

$3 x^{3}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

Step 7

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

$3 x^{3}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

Step 8

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

Step 9

Multiply the new quotient term by the divisor.

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $24 x^{3} - 96 x^{2}$

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

Step 11

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

Step 12

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

Step 13

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

Step 14

Multiply the new quotient term by the divisor.

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{2} - 16 x$

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

Step 16

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

Step 17

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

$64$

Step 18

Divide the highest order term in the dividend $16 x$ by the highest order term in divisor $2 x$ .

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

$64$

Step 19

Multiply the new quotient term by the divisor.

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

$64$

$16 x$

$64$

Step 20

The expression needs to be subtracted from the dividend, so change all the signs in $16 x - 64$

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

$64$

$16 x$

$64$

Step 21

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

$3 x^{3}$

$12 x^{2}$

$2 x$

$8$

$2 x$

$8$

$6 x^{4}$

$0 x^{3}$

$92 x^{2}$

$0 x$

$64$

$6 x^{4}$

$24 x^{3}$

$92 x^{2}$

$24 x^{3}$

$96 x^{2}$

$4 x^{2}$

$0 x$

$4 x^{2}$

$16 x$

$64$

$16 x$

$64$

$0$

Step 22

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

$3 x^{3} + 12 x^{2} + 2 x + 8$