Divide Using Long Polynomial Division (7x^8+8x^4+x^2)/x

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

Step 1

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

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

Step 2

Divide the highest order term in the dividend $7 x^{8}$ by the highest order term in divisor $x$ .

$7 x^{7}$

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$7 x^{7}$

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

$7 x^{8}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $7 x^{8} + 0$

$7 x^{7}$

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

$7 x^{8}$

$0$

Step 5

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

$7 x^{7}$

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

$7 x^{8}$

$0$

Step 6

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

$7 x^{7}$

$x$

$0$

$7 x^{8}$

$0 x^{7}$

$0 x^{6}$

$0 x^{5}$

$8 x^{4}$

$0 x^{3}$

$x^{2}$

$0 x$

$0$

$7 x^{8}$

$0$

$0 x^{6}$

$0 x^{5}$

Step 7

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

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

Divide Using Long Polynomial Division (7x^8+8x^4+x^2)/x

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