Algebra Examples

$(8 x^{2} + 2 x^{3} + 3) \div (x^{2} + 2 x - 1)$

Step 1

Reorder $8 x^{2}$ and $2 x^{3}$ .

$\frac{2 x^{3} + 8 x^{2} + 3}{x^{2} + 2 x - 1}$

Step 2

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

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

Step 3

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

$2 x$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

Step 4

Multiply the new quotient term by the divisor.

$2 x$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

Step 5

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

$2 x$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

Step 6

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

$2 x$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

Step 7

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

$2 x$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

$3$

Step 8

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

$2 x$

$4$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

$3$

Step 9

Multiply the new quotient term by the divisor.

$2 x$

$4$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

$3$

$4 x^{2}$

$8 x$

$4$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $4 x^{2} + 8 x - 4$

$2 x$

$4$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

$3$

$4 x^{2}$

$8 x$

$4$

Step 11

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

$2 x$

$4$

$x^{2}$

$2 x$

$1$

$2 x^{3}$

$8 x^{2}$

$0 x$

$3$

$2 x^{3}$

$4 x^{2}$

$2 x$

$4 x^{2}$

$2 x$

$3$

$4 x^{2}$

$8 x$

$4$

$6 x$

$7$

Step 12

The quotient is $2 x + 4$ .

$2 x + 4$