Pre-Algebra Examples

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

Step 1

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

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

Step 2

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

$x^{3}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

Step 3

Multiply the new quotient term by the divisor.

$x^{3}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{4} - 3 x^{3}$

$x^{3}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

Step 5

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

$x^{3}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

Step 6

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

$x^{3}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

Step 7

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

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

Step 8

Multiply the new quotient term by the divisor.

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{2} - 6 x$

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

Step 10

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

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

Step 11

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

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

$9$

Step 12

Divide the highest order term in the dividend $6 x$ by the highest order term in divisor $2 x$ .

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

$9$

Step 13

Multiply the new quotient term by the divisor.

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

$9$

$6 x$

$9$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $6 x - 9$

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

$9$

$6 x$

$9$

Step 15

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

$x^{3}$

$0 x^{2}$

$2 x$

$3$

$2 x$

$3$

$2 x^{4}$

$3 x^{3}$

$4 x^{2}$

$0 x$

$9$

$2 x^{4}$

$3 x^{3}$

$0$

$4 x^{2}$

$0 x$

$4 x^{2}$

$6 x$

$9$

$6 x$

$9$

$0$

Step 16

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

$x^{3} + 0 x^{2} + 2 x + 3$