Pre-Algebra Examples

$\frac{x^{12} - 2 x^{7} + 6 x^{2} - 4}{x + 1}$

Step 1

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

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

Step 2

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

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

Step 3

Multiply the new quotient term by the divisor.

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $x^{12} + x^{11}$

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

Step 5

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

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

Step 6

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

$x^{11}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

Step 7

Divide the highest order term in the dividend $- x^{11}$ by the highest order term in divisor $x$ .

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

Step 8

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- x^{11} - x^{10}$

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

Step 10

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

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

Step 11

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

$x^{11}$

$x^{10}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

Step 12

Divide the highest order term in the dividend $x^{10}$ by the highest order term in divisor $x$ .

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

Step 13

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $x^{10} + x^{9}$

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

Step 15

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

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

Step 16

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

$x^{11}$

$x^{10}$

$x^{9}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

Step 17

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

Step 18

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $- x^{9} - x^{8}$

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

Step 20

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

Step 21

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

Step 22

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

Step 23

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

Step 24

The expression needs to be subtracted from the dividend, so change all the signs in $x^{8} + x^{7}$

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

Step 25

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

Step 26

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

Step 27

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

Step 28

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

Step 29

The expression needs to be subtracted from the dividend, so change all the signs in $- 3 x^{7} - 3 x^{6}$

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

Step 30

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

Step 31

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

Step 32

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

Step 33

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

Step 34

The expression needs to be subtracted from the dividend, so change all the signs in $3 x^{6} + 3 x^{5}$

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

Step 35

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

Step 36

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

Step 37

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

Step 38

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

Step 39

The expression needs to be subtracted from the dividend, so change all the signs in $- 3 x^{5} - 3 x^{4}$

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

Step 40

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

Step 41

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

Step 42

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

Step 43

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

Step 44

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

Step 45

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

Step 46

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

Step 47

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

Step 48

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

Step 49

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

Step 50

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

Step 51

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

Step 52

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

Step 53

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

Step 54

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

Step 55

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

Step 56

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

Step 57

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

Step 58

Multiply the new quotient term by the divisor.

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

Step 59

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

Step 60

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

$x^{11}$

$x^{10}$

$x^{9}$

$x^{8}$

$x^{7}$

$3 x^{6}$

$3 x^{5}$

$3 x^{4}$

$3 x^{3}$

$3 x^{2}$

$9 x$

$9$

$x$

$1$

$x^{12}$

$0 x^{11}$

$0 x^{10}$

$0 x^{9}$

$0 x^{8}$

$2 x^{7}$

$0 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$6 x^{2}$

$0 x$

$4$

$x^{12}$

$x^{11}$

$0 x^{10}$

$x^{11}$

$x^{10}$

$0 x^{9}$

$x^{10}$

$x^{9}$

$0 x^{8}$

$x^{9}$

$x^{8}$

$2 x^{7}$

$x^{8}$

$x^{7}$

$3 x^{7}$

$0 x^{6}$

$3 x^{7}$

$3 x^{6}$

$0 x^{5}$

$3 x^{6}$

$3 x^{5}$

$0 x^{4}$

$3 x^{5}$

$3 x^{4}$

$0 x^{3}$

$3 x^{4}$

$3 x^{3}$

$6 x^{2}$

$3 x^{3}$

$3 x^{2}$

$9 x^{2}$

$0 x$

$9 x^{2}$

$9 x$

$4$

$9 x$

$9$

$5$

Step 61

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

$x^{11} - x^{10} + x^{9} - x^{8} + x^{7} - 3 x^{6} + 3 x^{5} - 3 x^{4} + 3 x^{3} - 3 x^{2} + 9 x - 9 + \frac{5}{x + 1}$