Algebra Examples

$(- 4 x^{3} + 35 x + 25) \div (- 2 x - 5)$

Step 1

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

$2 x$

$5$

$4 x^{3}$

$0 x^{2}$

$35 x$

$25$

Step 2

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

					$2 x^{2}$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$

Step 3

Multiply the new quotient term by the divisor.

					$2 x^{2}$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				-	$4 x^{3}$	-	$10 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $- 4 x^{3} - 10 x^{2}$

					$2 x^{2}$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$

Step 5

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

					$2 x^{2}$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$

Step 6

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

					$2 x^{2}$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$

Step 7

Divide the highest order term in the dividend $10 x^{2}$ by the highest order term in divisor $- 2 x$ .

					$2 x^{2}$	-	$5 x$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$

Step 8

Multiply the new quotient term by the divisor.

					$2 x^{2}$	-	$5 x$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						+	$10 x^{2}$	+	$25 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $10 x^{2} + 25 x$

					$2 x^{2}$	-	$5 x$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$

Step 10

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

					$2 x^{2}$	-	$5 x$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$

Step 11

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

					$2 x^{2}$	-	$5 x$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$	+	$25$

Step 12

Divide the highest order term in the dividend $10 x$ by the highest order term in divisor $- 2 x$ .

					$2 x^{2}$	-	$5 x$	-	$5$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$	+	$25$

Step 13

Multiply the new quotient term by the divisor.

					$2 x^{2}$	-	$5 x$	-	$5$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$	+	$25$
								+	$10 x$	+	$25$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $10 x + 25$

					$2 x^{2}$	-	$5 x$	-	$5$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$	+	$25$
								-	$10 x$	-	$25$

Step 15

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

					$2 x^{2}$	-	$5 x$	-	$5$
-	$2 x$	-	$5$	-	$4 x^{3}$	+	$0 x^{2}$	+	$35 x$	+	$25$
				+	$4 x^{3}$	+	$10 x^{2}$
						+	$10 x^{2}$	+	$35 x$
						-	$10 x^{2}$	-	$25 x$
								+	$10 x$	+	$25$
								-	$10 x$	-	$25$
											$0$

Step 16

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

$2 x^{2} - 5 x - 5$