Algebra Examples

$(27 x^{4} - 18 x^{3} + 9 x^{2}) \div 3 x$

Step 1

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

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

Step 2

Divide the highest order term in the dividend $27 x^{4}$ by the highest order term in divisor $3 x$ .

$9 x^{3}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$9 x^{3}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $27 x^{4} + 0$

$9 x^{3}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

Step 5

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

$9 x^{3}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

Step 6

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

$9 x^{3}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

Step 7

Divide the highest order term in the dividend $- 18 x^{3}$ by the highest order term in divisor $3 x$ .

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

Step 8

Multiply the new quotient term by the divisor.

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 18 x^{3} + 0$

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

Step 10

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

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

Step 11

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

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

Step 12

Divide the highest order term in the dividend $9 x^{2}$ by the highest order term in divisor $3 x$ .

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

Step 13

Multiply the new quotient term by the divisor.

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

$9 x^{2}$

$0$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $9 x^{2} + 0$

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

$9 x^{2}$

$0$

Step 15

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

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

$9 x^{2}$

$0$

Step 16

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

$9 x^{3}$

$6 x^{2}$

$3 x$

$0$

$27 x^{4}$

$18 x^{3}$

$9 x^{2}$

$0 x$

$0$

$27 x^{4}$

$0$

$18 x^{3}$

$9 x^{2}$

$18 x^{3}$

$0$

$9 x^{2}$

$0 x$

$9 x^{2}$

$0$

Step 17

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

$9 x^{3} - 6 x^{2} + 3 x$