Algebra Examples

$(125 - 8 x^{3}) \div (25 + 10 x + 4 x^{2})$

Step 1

Reorder $125$ and $- 8 x^{3}$ .

$\frac{- 8 x^{3} + 125}{25 + 10 x + 4 x^{2}}$

Step 2

Expand $25 + 10 x + 4 x^{2}$ .

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Step 2.1

Reorder $25$ and $10 x$ .

$\frac{- 8 x^{3} + 125}{10 x + 25 + 4 x^{2}}$

Step 2.2

Move $25$ .

$\frac{- 8 x^{3} + 125}{10 x + 4 x^{2} + 25}$

Step 2.3

Reorder $10 x$ and $4 x^{2}$ .

$\frac{- 8 x^{3} + 125}{4 x^{2} + 10 x + 25}$

Step 3

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

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

Step 4

Divide the highest order term in the dividend $- 8 x^{3}$ by the highest order term in divisor $4 x^{2}$ .

$2 x$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

Step 5

Multiply the new quotient term by the divisor.

$2 x$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

Step 6

The expression needs to be subtracted from the dividend, so change all the signs in $- 8 x^{3} - 20 x^{2} - 50 x$

$2 x$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

Step 7

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

$2 x$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

Step 8

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

$2 x$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

$125$

Step 9

Divide the highest order term in the dividend $20 x^{2}$ by the highest order term in divisor $4 x^{2}$ .

$2 x$

$5$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

$125$

Step 10

Multiply the new quotient term by the divisor.

$2 x$

$5$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

$125$

$20 x^{2}$

$50 x$

$125$

Step 11

The expression needs to be subtracted from the dividend, so change all the signs in $20 x^{2} + 50 x + 125$

$2 x$

$5$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

$125$

$20 x^{2}$

$50 x$

$125$

Step 12

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

$2 x$

$5$

$4 x^{2}$

$10 x$

$25$

$8 x^{3}$

$0 x^{2}$

$0 x$

$125$

$8 x^{3}$

$20 x^{2}$

$50 x$

$20 x^{2}$

$50 x$

$125$

$20 x^{2}$

$50 x$

$125$

$0$

Step 13

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

$- 2 x + 5$