Basic Math Examples

$\frac{6 c^{4} - 12 c^{2} + 18 c + 19}{6 c + 6}$

Step 1

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

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

Step 2

Divide the highest order term in the dividend $6 c^{4}$ by the highest order term in divisor $6 c$ .

$c^{3}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

Step 3

Multiply the new quotient term by the divisor.

$c^{3}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $6 c^{4} + 6 c^{3}$

$c^{3}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

Step 5

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

$c^{3}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

Step 6

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

$c^{3}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

Step 7

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

$c^{3}$

$c^{2}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

Step 8

Multiply the new quotient term by the divisor.

$c^{3}$

$c^{2}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 c^{3} - 6 c^{2}$

$c^{3}$

$c^{2}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

Step 10

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

$c^{3}$

$c^{2}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

Step 11

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

$c^{3}$

$c^{2}$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

Step 12

Divide the highest order term in the dividend $- 6 c^{2}$ by the highest order term in divisor $6 c$ .

$c^{3}$

$c^{2}$

$c$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

Step 13

Multiply the new quotient term by the divisor.

$c^{3}$

$c^{2}$

$c$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 c^{2} - 6 c$

$c^{3}$

$c^{2}$

$c$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

Step 15

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

$c^{3}$

$c^{2}$

$c$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

Step 16

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

$c^{3}$

$c^{2}$

$c$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

$19$

Step 17

Divide the highest order term in the dividend $24 c$ by the highest order term in divisor $6 c$ .

$c^{3}$

$c^{2}$

$c$

$4$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

$19$

Step 18

Multiply the new quotient term by the divisor.

$c^{3}$

$c^{2}$

$c$

$4$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

$19$

$24 c$

$24$

Step 19

The expression needs to be subtracted from the dividend, so change all the signs in $24 c + 24$

$c^{3}$

$c^{2}$

$c$

$4$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

$19$

$24 c$

$24$

Step 20

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

$c^{3}$

$c^{2}$

$c$

$4$

$6 c$

$6$

$6 c^{4}$

$0 c^{3}$

$12 c^{2}$

$18 c$

$19$

$6 c^{4}$

$6 c^{3}$

$12 c^{2}$

$6 c^{3}$

$6 c^{2}$

$18 c$

$6 c^{2}$

$6 c$

$24 c$

$19$

$24 c$

$24$

$5$

Step 21

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

$c^{3} - c^{2} - c + 4 - \frac{5}{6 c + 6}$