Divide Using Long Polynomial Division (x^4-6x^2-27)÷(x+3)

$(x^{4} - 6 x^{2} - 27) \div (x + 3)$

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

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

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

$x^{3}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

Multiply the new quotient term by the divisor.

$x^{3}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

$x^{4}$

$3 x^{3}$

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

$x^{3}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

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

$x^{3}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

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

$x^{3}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

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

$x^{3}$

–

$3 x^{2}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

Multiply the new quotient term by the divisor.

$x^{3}$

–

$3 x^{2}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

–

$3 x^{3}$

–

$9 x^{2}$

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

$x^{3}$

–

$3 x^{2}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

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

$x^{3}$

–

$3 x^{2}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

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

$x^{3}$

–

$3 x^{2}$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

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

$x^{3}$

–

$3 x^{2}$

$3 x$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

Multiply the new quotient term by the divisor.

$x^{3}$

–

$3 x^{2}$

$3 x$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

$3 x^{2}$

$9 x$

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

$x^{3}$

–

$3 x^{2}$

$3 x$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

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

$x^{3}$

–

$3 x^{2}$

$3 x$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

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

$x^{3}$

–

$3 x^{2}$

$3 x$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

–

$27$

Divide the highest order term in the dividend $- 9 x$ by the highest order term in divisor $x$ .

$x^{3}$

–

$3 x^{2}$

$3 x$

–

$9$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

–

$27$

Multiply the new quotient term by the divisor.

$x^{3}$

–

$3 x^{2}$

$3 x$

–

$9$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

–

$27$

–

$9 x$

–

$27$

The expression needs to be subtracted from the dividend, so change all the signs in $- 9 x - 27$

$x^{3}$

–

$3 x^{2}$

$3 x$

–

$9$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

–

$27$

$9 x$

$27$

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

$x^{3}$

–

$3 x^{2}$

$3 x$

–

$9$

$x$

$3$

$x^{4}$

$0 x^{3}$

–

$6 x^{2}$

$0 x$

–

$27$

–

$x^{4}$

–

$3 x^{3}$

–

$3 x^{3}$

–

$6 x^{2}$

$3 x^{3}$

$9 x^{2}$

$3 x^{2}$

$0 x$

–

$3 x^{2}$

–

$9 x$

–

$9 x$

–

$27$

$9 x$

$27$

$0$

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

$x^{3} - 3 x^{2} + 3 x - 9$

Divide Using Long Polynomial Division (x^4-6x^2-27)÷(x+3)

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App from the store