Algebra Examples

$\frac{2 x^{5} + 5 x^{3}}{x}$

Step 1

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

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 2

Divide the highest order term in the dividend $2 x^{5}$ by the highest order term in divisor $x$ .

$2 x^{4}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

Step 3

Multiply the new quotient term by the divisor.

$2 x^{4}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{5} + 0$

$2 x^{4}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

Step 5

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

$2 x^{4}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

Step 6

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

$2 x^{4}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

Step 7

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

$2 x^{4}$

$0 x^{3}$

$5 x^{2}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

Step 8

Multiply the new quotient term by the divisor.

$2 x^{4}$

$0 x^{3}$

$5 x^{2}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

$5 x^{3}$

$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $5 x^{3} + 0$

$2 x^{4}$

$0 x^{3}$

$5 x^{2}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

$5 x^{3}$

$0$

Step 10

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

$2 x^{4}$

$0 x^{3}$

$5 x^{2}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

$5 x^{3}$

$0$

Step 11

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

$2 x^{4}$

$0 x^{3}$

$5 x^{2}$

$x$

$0$

$2 x^{5}$

$0 x^{4}$

$5 x^{3}$

$0 x^{2}$

$0 x$

$0$

$2 x^{5}$

$0$

$5 x^{3}$

$0 x^{2}$

$5 x^{3}$

$0$

$0 x$

$0$

Step 12

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

$2 x^{4} + 0 x^{3} + 5 x^{2}$