Divide Using Long Polynomial Division (x^5+11x^3-12)/(x-1)

$\frac{x^{5} + 11 x^{3} - 12}{x - 1}$

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

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

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

$x^{4}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

Multiply the new quotient term by the divisor.

$x^{4}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

The expression needs to be subtracted from the dividend, so change all the signs in $x^{5} - x^{4}$

$x^{4}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

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

$x^{4}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

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

$x^{4}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

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

$x^{4}$

$x^{3}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

Multiply the new quotient term by the divisor.

$x^{4}$

$x^{3}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

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

$x^{4}$

$x^{3}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

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

$x^{4}$

$x^{3}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

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

$x^{4}$

$x^{3}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

Divide the highest order term in the dividend $12 x^{3}$ by the highest order term in divisor $x$ .

$x^{4}$

$x^{3}$

$12 x^{2}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

Multiply the new quotient term by the divisor.

$x^{4}$

$x^{3}$

$12 x^{2}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{3} - 12 x^{2}$

$x^{4}$

$x^{3}$

$12 x^{2}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

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

$x^{4}$

$x^{3}$

$12 x^{2}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

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

$x^{4}$

$x^{3}$

$12 x^{2}$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

Divide the highest order term in the dividend $12 x^{2}$ by the highest order term in divisor $x$ .

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

Multiply the new quotient term by the divisor.

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

The expression needs to be subtracted from the dividend, so change all the signs in $12 x^{2} - 12 x$

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

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

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

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

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

$12$

Divide the highest order term in the dividend $12 x$ by the highest order term in divisor $x$ .

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$12$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

$12$

Multiply the new quotient term by the divisor.

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$12$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

$12$

$12 x$

$12$

The expression needs to be subtracted from the dividend, so change all the signs in $12 x - 12$

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$12$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

$12$

$12 x$

$12$

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

$x^{4}$

$x^{3}$

$12 x^{2}$

$12 x$

$12$

$x$

$1$

$x^{5}$

$0 x^{4}$

$11 x^{3}$

$0 x^{2}$

$0 x$

$12$

$x^{5}$

$x^{4}$

$11 x^{3}$

$x^{4}$

$x^{3}$

$12 x^{3}$

$0 x^{2}$

$12 x^{3}$

$12 x^{2}$

$0 x$

$12 x^{2}$

$12 x$

$12$

$12 x$

$12$

$0$

Since the remander is $0$ , the final answer is the quotient.

$x^{4} + x^{3} + 12 x^{2} + 12 x + 12$

Divide Using Long Polynomial Division (x^5+11x^3-12)/(x-1)

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