Algebra Examples

$(5 x^{3} - 25 x^{2} + 6 x^{4} - 30 x^{3}) \div (x + 5)$

Step 1

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

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$

Step 2

The first number in the dividend $(6)$ is put into the first position of the result area (below the horizontal line).

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$

	$6$

Step 3

Multiply the newest entry in the result $(6)$ by the divisor $(- 5)$ and place the result of $(- 30)$ under the next term in the dividend $(- 25)$ .

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$
	$6$

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.

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$
	$6$	$- 55$

Step 5

Multiply the newest entry in the result $(- 55)$ by the divisor $(- 5)$ and place the result of $(275)$ under the next term in the dividend $(- 25)$ .

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$
	$6$	$- 55$

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.

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$
	$6$	$- 55$	$250$

Step 7

Multiply the newest entry in the result $(250)$ by the divisor $(- 5)$ and place the result of $(- 1250)$ under the next term in the dividend $(0)$ .

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$	$- 1250$
	$6$	$- 55$	$250$

Step 8

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

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$	$- 1250$
	$6$	$- 55$	$250$	$- 1250$

Step 9

Multiply the newest entry in the result $(- 1250)$ by the divisor $(- 5)$ and place the result of $(6250)$ under the next term in the dividend $(0)$ .

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$	$- 1250$	$6250$
	$6$	$- 55$	$250$	$- 1250$

Step 10

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

$- 5$	$6$	$- 25$	$- 25$	$0$	$0$
		$- 30$	$275$	$- 1250$	$6250$
	$6$	$- 55$	$250$	$- 1250$	$6250$

Step 11

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

$6 x^{3} + - 55 x^{2} + (250) x - 1250 + \frac{6250}{x + 5}$

Step 12

Simplify the quotient polynomial.

$6 x^{3} - 55 x^{2} + 250 x - 1250 + \frac{6250}{x + 5}$