Finite Math Examples

$\frac{- 15 x^{9} + 25 x^{6}}{- 5 x^{3}}$

Step 1

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

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 2

Divide the highest order term in the dividend $- 15 x^{9}$ by the highest order term in divisor $- 5 x^{3}$ .

$3 x^{6}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$3 x^{6}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $- 15 x^{9} + 0 + 0 + 0$

$3 x^{6}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

Step 5

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

$3 x^{6}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

Step 6

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

$3 x^{6}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

Step 7

Divide the highest order term in the dividend $25 x^{6}$ by the highest order term in divisor $- 5 x^{3}$ .

$3 x^{6}$

$0 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

Step 8

Multiply the new quotient term by the divisor.

$3 x^{6}$

$0 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$25 x^{6}$

$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $25 x^{6} + 0 + 0 + 0$

$3 x^{6}$

$0 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$25 x^{6}$

$0$

Step 10

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

$3 x^{6}$

$0 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$25 x^{6}$

$0$

Step 11

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

$3 x^{6}$

$0 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0 x^{8}$

$0 x^{7}$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$0 x^{2}$

$0 x$

$0$

$15 x^{9}$

$0$

$25 x^{6}$

$0 x^{5}$

$0 x^{4}$

$0 x^{3}$

$25 x^{6}$

$0$

$0 x^{2}$

$0 x$

$0$

Step 12

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

$3 x^{6} + 0 x^{5} + 0 x^{4} - 5 x^{3}$