Algebra Examples

$(2 x^{2} + 13 x - 8) \div (x - \frac{1}{2})$

Step 1

Place the numbers representing the divisor and the dividend into a division-like configuration.

$\frac{1}{2}$	$2$	$13$	$- 8$

Step 2

The first number in the dividend $(2)$ is put into the first position of the result area (below the horizontal line).

$\frac{1}{2}$	$2$	$13$	$- 8$

	$2$

Step 3

Multiply the newest entry in the result $(2)$ by the divisor $(\frac{1}{2})$ and place the result of $(1)$ under the next term in the dividend $(13)$ .

$\frac{1}{2}$	$2$	$13$	$- 8$
		$1$
	$2$

Step 4

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{1}{2}$	$2$	$13$	$- 8$
		$1$
	$2$	$14$

Step 5

Multiply the newest entry in the result $(14)$ by the divisor $(\frac{1}{2})$ and place the result of $(7)$ under the next term in the dividend $(- 8)$ .

$\frac{1}{2}$	$2$	$13$	$- 8$
		$1$	$7$
	$2$	$14$

Step 6

Add the product of the multiplication and the number from the dividend and put the result in the next position on the result line.

$\frac{1}{2}$	$2$	$13$	$- 8$
		$1$	$7$
	$2$	$14$	$- 1$

Step 7

All numbers except the last become the coefficients of the quotient polynomial. The last value in the result line is the remainder.

$(2) x + 14 + \frac{- 1}{x - \frac{1}{2}}$

Step 8

Simplify the quotient polynomial.

$2 x + 14 - \frac{2}{2 x - 1}$