Algebra Examples

$\frac{8 x^{8} - 8 x^{2} - 28 x}{4 x}$

Step 1

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

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

Step 2

Divide the highest order term in the dividend $8 x^{8}$ by the highest order term in divisor $4 x$ .

$2 x^{7}$

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$2 x^{7}$

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

$8 x^{8}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{8} + 0$

$2 x^{7}$

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

$8 x^{8}$

$0$

Step 5

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

$2 x^{7}$

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

$8 x^{8}$

$0$

Step 6

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

$2 x^{7}$

$4 x$

$0$

$8 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$8 x^{2}$

$28 x$

$0$

$8 x^{8}$

$0$

$0 x^{6}$

$0 x^{5}$

Step 7

The final answer is the quotient plus the remainder over the divisor.

$2 x^{7} + \frac{- 8 x^{2} - 28 x}{4 x}$