Algebra Examples

$\frac{(- 150 x^{2} + 15 x^{4} + 135)}{(3 x + 9)}$

Step 1

Reorder $- 150 x^{2}$ and $15 x^{4}$ .

$\frac{15 x^{4} - 150 x^{2} + 135}{3 x + 9}$

Step 2

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

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

Step 3

Divide the highest order term in the dividend $15 x^{4}$ by the highest order term in divisor $3 x$ .

$5 x^{3}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

Step 4

Multiply the new quotient term by the divisor.

$5 x^{3}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $15 x^{4} + 45 x^{3}$

$5 x^{3}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

Step 6

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

$5 x^{3}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

Step 7

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

$5 x^{3}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

Step 8

Divide the highest order term in the dividend $- 45 x^{3}$ by the highest order term in divisor $3 x$ .

$5 x^{3}$

$15 x^{2}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

Step 9

Multiply the new quotient term by the divisor.

$5 x^{3}$

$15 x^{2}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 45 x^{3} - 135 x^{2}$

$5 x^{3}$

$15 x^{2}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

Step 11

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

$5 x^{3}$

$15 x^{2}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

Step 12

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

$5 x^{3}$

$15 x^{2}$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

Step 13

Divide the highest order term in the dividend $- 15 x^{2}$ by the highest order term in divisor $3 x$ .

$5 x^{3}$

$15 x^{2}$

$5 x$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

Step 14

Multiply the new quotient term by the divisor.

$5 x^{3}$

$15 x^{2}$

$5 x$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $- 15 x^{2} - 45 x$

$5 x^{3}$

$15 x^{2}$

$5 x$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

Step 16

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

$5 x^{3}$

$15 x^{2}$

$5 x$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

Step 17

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

$5 x^{3}$

$15 x^{2}$

$5 x$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

$135$

Step 18

Divide the highest order term in the dividend $45 x$ by the highest order term in divisor $3 x$ .

$5 x^{3}$

$15 x^{2}$

$5 x$

$15$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

$135$

Step 19

Multiply the new quotient term by the divisor.

$5 x^{3}$

$15 x^{2}$

$5 x$

$15$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

$135$

$45 x$

$135$

Step 20

The expression needs to be subtracted from the dividend, so change all the signs in $45 x + 135$

$5 x^{3}$

$15 x^{2}$

$5 x$

$15$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

$135$

$45 x$

$135$

Step 21

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

$5 x^{3}$

$15 x^{2}$

$5 x$

$15$

$3 x$

$9$

$15 x^{4}$

$0 x^{3}$

$150 x^{2}$

$0 x$

$135$

$15 x^{4}$

$45 x^{3}$

$150 x^{2}$

$45 x^{3}$

$135 x^{2}$

$15 x^{2}$

$0 x$

$15 x^{2}$

$45 x$

$135$

$45 x$

$135$

$0$

Step 22

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

$5 x^{3} - 15 x^{2} - 5 x + 15$