Algebra Examples

$(x^{3} + 250 x^{2} + 100 x) \div (\frac{1}{2} x^{2} + 25 x + 9)$

Step 1

Combine $\frac{1}{2}$ and $x^{2}$ .

$\frac{x^{3} + 250 x^{2} + 100 x}{\frac{x^{2}}{2} + 25 x + 9}$

Step 2

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

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

Step 3

Divide the highest order term in the dividend $x^{3}$ by the highest order term in divisor $\frac{x^{2}}{2}$ .

$2 x$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

Step 4

Multiply the new quotient term by the divisor.

$2 x$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $x^{3} + 50 x^{2} + 18 x$

$2 x$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

Step 6

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

$2 x$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

Step 7

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

$2 x$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

$0$

Step 8

Divide the highest order term in the dividend $200 x^{2}$ by the highest order term in divisor $\frac{x^{2}}{2}$ .

$2 x$

$400$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

$0$

Step 9

Multiply the new quotient term by the divisor.

$2 x$

$400$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

$0$

$200 x^{2}$

$10000 x$

$3600$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $200 x^{2} + 10000 x + 3600$

$2 x$

$400$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

$0$

$200 x^{2}$

$10000 x$

$3600$

Step 11

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

$2 x$

$400$

$\frac{x^{2}}{2}$

$25 x$

$9$

$x^{3}$

$250 x^{2}$

$100 x$

$0$

$x^{3}$

$50 x^{2}$

$18 x$

$200 x^{2}$

$82 x$

$0$

$200 x^{2}$

$10000 x$

$3600$

$9918 x$

$3600$

Step 12

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

$2 x + 400 + \frac{- 9918 x - 3600}{\frac{x^{2}}{2} + 25 x + 9}$