Divide Using Long Polynomial Division (-25x^3+35x^2-2x-6)÷(5x-3)

$(- 25 x^{3} + 35 x^{2} - 2 x - 6) \div (5 x - 3)$

Step 1

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

$5 x$

$3$

$25 x^{3}$

$35 x^{2}$

$2 x$

$6$

Step 2

Divide the highest order term in the dividend $- 25 x^{3}$ by the highest order term in divisor $5 x$ .

				-	$5 x^{2}$
	$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$

Step 3

Multiply the new quotient term by the divisor.

			-	$5 x^{2}$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			-	$25 x^{3}$	+	$15 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $- 25 x^{3} + 15 x^{2}$

			-	$5 x^{2}$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$

Step 5

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

			-	$5 x^{2}$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$

Step 6

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

			-	$5 x^{2}$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$

Step 7

Divide the highest order term in the dividend $20 x^{2}$ by the highest order term in divisor $5 x$ .

			-	$5 x^{2}$	+	$4 x$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$

Step 8

Multiply the new quotient term by the divisor.

			-	$5 x^{2}$	+	$4 x$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					+	$20 x^{2}$	-	$12 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $20 x^{2} - 12 x$

			-	$5 x^{2}$	+	$4 x$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$

Step 10

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

			-	$5 x^{2}$	+	$4 x$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$

Step 11

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

			-	$5 x^{2}$	+	$4 x$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$	-	$6$

Step 12

Divide the highest order term in the dividend $10 x$ by the highest order term in divisor $5 x$ .

			-	$5 x^{2}$	+	$4 x$	+	$2$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$	-	$6$

Step 13

Multiply the new quotient term by the divisor.

			-	$5 x^{2}$	+	$4 x$	+	$2$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$	-	$6$
							+	$10 x$	-	$6$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $10 x - 6$

			-	$5 x^{2}$	+	$4 x$	+	$2$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$	-	$6$
							-	$10 x$	+	$6$

Step 15

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

			-	$5 x^{2}$	+	$4 x$	+	$2$
$5 x$	-	$3$	-	$25 x^{3}$	+	$35 x^{2}$	-	$2 x$	-	$6$
			+	$25 x^{3}$	-	$15 x^{2}$
					+	$20 x^{2}$	-	$2 x$
					-	$20 x^{2}$	+	$12 x$
							+	$10 x$	-	$6$
							-	$10 x$	+	$6$
										$0$

Step 16

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

$- 5 x^{2} + 4 x + 2$

Divide Using Long Polynomial Division (-25x^3+35x^2-2x-6)÷(5x-3)

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