Divide Using Long Polynomial Division (-14x^7+8x^5-6x^4+5x)/(x^3)

$\frac{- 14 x^{7} + 8 x^{5} - 6 x^{4} + 5 x}{x^{3}}$

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

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

Divide the highest order term in the dividend $- 14 x^{7}$ by the highest order term in divisor $x^{3}$ .

–

$14 x^{4}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

Multiply the new quotient term by the divisor.

–

$14 x^{4}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

–

$14 x^{7}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $- 14 x^{7} + 0 + 0 + 0$

–

$14 x^{4}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

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

–

$14 x^{4}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

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

–

$14 x^{4}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

Divide the highest order term in the dividend $8 x^{5}$ by the highest order term in divisor $x^{3}$ .

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

Multiply the new quotient term by the divisor.

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$8 x^{5}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $8 x^{5} + 0 + 0 + 0$

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

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

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

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

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

Divide the highest order term in the dividend $- 6 x^{4}$ by the highest order term in divisor $x^{3}$ .

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

–

$6 x$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

Multiply the new quotient term by the divisor.

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

–

$6 x$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

–

$6 x^{4}$

$0$

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 x^{4} + 0 + 0 + 0$

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

–

$6 x$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

$6 x^{4}$

–

$0$

–

$0$

–

$0$

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

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

–

$6 x$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

$6 x^{4}$

–

$0$

–

$0$

–

$0$

$5 x$

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

–

$14 x^{4}$

$0 x^{3}$

$8 x^{2}$

–

$6 x$

$x^{3}$

$0 x^{2}$

$0 x$

$0$

–

$14 x^{7}$

$0 x^{6}$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

$5 x$

$0$

$14 x^{7}$

–

$0$

–

$0$

–

$0$

$8 x^{5}$

–

$6 x^{4}$

$0 x^{3}$

$0 x^{2}$

–

$8 x^{5}$

–

$0$

–

$0$

–

$0$

–

$6 x^{4}$

$0$

$5 x$

$0$

$6 x^{4}$

–

$0$

–

$0$

–

$0$

$5 x$

$0$

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

$- 14 x^{4} + 8 x^{2} - 6 x + \frac{5 x}{x^{3}}$

Divide Using Long Polynomial Division (-14x^7+8x^5-6x^4+5x)/(x^3)

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Create a High Performed UI/UX Design from a Silicon Valley.

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App from the store