Algebra Examples

$\frac{4 p^{4} - 17 p^{2} + 14 p - 3}{2 p - 3}$

Step 1

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

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

Step 2

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

$2 p^{3}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

Step 3

Multiply the new quotient term by the divisor.

$2 p^{3}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

Step 4

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

$2 p^{3}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

Step 5

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

$2 p^{3}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

Step 6

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

$2 p^{3}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

Step 7

Divide the highest order term in the dividend $6 p^{3}$ by the highest order term in divisor $2 p$ .

$2 p^{3}$

$3 p^{2}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

Step 8

Multiply the new quotient term by the divisor.

$2 p^{3}$

$3 p^{2}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $6 p^{3} - 9 p^{2}$

$2 p^{3}$

$3 p^{2}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

Step 10

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

$2 p^{3}$

$3 p^{2}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

Step 11

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

$2 p^{3}$

$3 p^{2}$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

Step 12

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

$2 p^{3}$

$3 p^{2}$

$4 p$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

Step 13

Multiply the new quotient term by the divisor.

$2 p^{3}$

$3 p^{2}$

$4 p$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 p^{2} + 12 p$

$2 p^{3}$

$3 p^{2}$

$4 p$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

Step 15

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

$2 p^{3}$

$3 p^{2}$

$4 p$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

Step 16

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

$2 p^{3}$

$3 p^{2}$

$4 p$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

$3$

Step 17

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

$2 p^{3}$

$3 p^{2}$

$4 p$

$1$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

$3$

Step 18

Multiply the new quotient term by the divisor.

$2 p^{3}$

$3 p^{2}$

$4 p$

$1$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

$3$

$2 p$

$3$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $2 p - 3$

$2 p^{3}$

$3 p^{2}$

$4 p$

$1$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

$3$

$2 p$

$3$

Step 20

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

$2 p^{3}$

$3 p^{2}$

$4 p$

$1$

$2 p$

$3$

$4 p^{4}$

$0 p^{3}$

$17 p^{2}$

$14 p$

$3$

$4 p^{4}$

$6 p^{3}$

$17 p^{2}$

$6 p^{3}$

$9 p^{2}$

$8 p^{2}$

$14 p$

$8 p^{2}$

$12 p$

$2 p$

$3$

$2 p$

$3$

$0$

Step 21

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

$2 p^{3} + 3 p^{2} - 4 p + 1$