Divide (-9x^4+4x^2+15-14x^3)÷(-x^2-x+2)

$(- 9 x^{4} + 4 x^{2} + 15 - 14 x^{3}) \div (- x^{2} - x + 2)$

Expand $- 9 x^{4} + 4 x^{2} + 15 - 14 x^{3}$ .

Move $15$ .

$\frac{- 9 x^{4} + 4 x^{2} - 14 x^{3} + 15}{- x^{2} - x + 2}$

Move $4 x^{2}$ .

$\frac{- 9 x^{4} - 14 x^{3} + 4 x^{2} + 15}{- x^{2} - x + 2}$

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

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

Divide the highest order term in the dividend $- 9 x^{4}$ by the highest order term in divisor $- x^{2}$ .

$9 x^{2}$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

Multiply the new quotient term by the divisor.

$9 x^{2}$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

The expression needs to be subtracted from the dividend, so change all the signs in $- 9 x^{4} - 9 x^{3} + 18 x^{2}$

$9 x^{2}$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

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

$9 x^{2}$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

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

$9 x^{2}$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

Divide the highest order term in the dividend $- 5 x^{3}$ by the highest order term in divisor $- x^{2}$ .

$9 x^{2}$

$5 x$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

Multiply the new quotient term by the divisor.

$9 x^{2}$

$5 x$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

The expression needs to be subtracted from the dividend, so change all the signs in $- 5 x^{3} - 5 x^{2} + 10 x$

$9 x^{2}$

$5 x$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

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

$9 x^{2}$

$5 x$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

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

$9 x^{2}$

$5 x$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

$15$

Divide the highest order term in the dividend $- 9 x^{2}$ by the highest order term in divisor $- x^{2}$ .

$9 x^{2}$

$5 x$

$9$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

$15$

Multiply the new quotient term by the divisor.

$9 x^{2}$

$5 x$

$9$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

$15$

$9 x^{2}$

$9 x$

$18$

The expression needs to be subtracted from the dividend, so change all the signs in $- 9 x^{2} - 9 x + 18$

$9 x^{2}$

$5 x$

$9$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

$15$

$9 x^{2}$

$9 x$

$18$

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

$9 x^{2}$

$5 x$

$9$

$x^{2}$

$x$

$2$

$9 x^{4}$

$14 x^{3}$

$4 x^{2}$

$0 x$

$15$

$9 x^{4}$

$9 x^{3}$

$18 x^{2}$

$5 x^{3}$

$14 x^{2}$

$0 x$

$5 x^{3}$

$5 x^{2}$

$10 x$

$9 x^{2}$

$10 x$

$15$

$9 x^{2}$

$9 x$

$18$

$x$

$3$

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

$9 x^{2} + 5 x + 9 + \frac{- x - 3}{- x^{2} - x + 2}$

Divide (-9x^4+4x^2+15-14x^3)÷(-x^2-x+2)

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