Divide Using Long Polynomial Division (50x^3+10x^2-35x-7)÷(5x-4)

$(50 x^{3} + 10 x^{2} - 35 x - 7) \div (5 x - 4)$

Step 1

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

$5 x$

$4$

$50 x^{3}$

$10 x^{2}$

$35 x$

$7$

Step 2

Divide the highest order term in the dividend $50 x^{3}$ by the highest order term in divisor $5 x$ .

					$10 x^{2}$
	$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$

Step 3

Multiply the new quotient term by the divisor.

				$10 x^{2}$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			+	$50 x^{3}$	-	$40 x^{2}$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $50 x^{3} - 40 x^{2}$

				$10 x^{2}$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$

Step 5

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

				$10 x^{2}$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$

Step 6

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

				$10 x^{2}$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$

Step 7

Divide the highest order term in the dividend $50 x^{2}$ by the highest order term in divisor $5 x$ .

				$10 x^{2}$	+	$10 x$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$

Step 8

Multiply the new quotient term by the divisor.

				$10 x^{2}$	+	$10 x$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					+	$50 x^{2}$	-	$40 x$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $50 x^{2} - 40 x$

				$10 x^{2}$	+	$10 x$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$

Step 10

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

				$10 x^{2}$	+	$10 x$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$

Step 11

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

				$10 x^{2}$	+	$10 x$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$	-	$7$

Step 12

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

				$10 x^{2}$	+	$10 x$	+	$1$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$	-	$7$

Step 13

Multiply the new quotient term by the divisor.

				$10 x^{2}$	+	$10 x$	+	$1$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$	-	$7$
							+	$5 x$	-	$4$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $5 x - 4$

				$10 x^{2}$	+	$10 x$	+	$1$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$	-	$7$
							-	$5 x$	+	$4$

Step 15

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

				$10 x^{2}$	+	$10 x$	+	$1$
$5 x$	-	$4$		$50 x^{3}$	+	$10 x^{2}$	-	$35 x$	-	$7$
			-	$50 x^{3}$	+	$40 x^{2}$
					+	$50 x^{2}$	-	$35 x$
					-	$50 x^{2}$	+	$40 x$
							+	$5 x$	-	$7$
							-	$5 x$	+	$4$
									-	$3$

Step 16

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

$10 x^{2} + 10 x + 1 - \frac{3}{5 x - 4}$

Divide Using Long Polynomial Division (50x^3+10x^2-35x-7)÷(5x-4)

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