Algebra Examples

$\frac{28 x^{3} + 42 x^{2} - 35 x}{7 x}$

Step 1

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

$7 x$

$0$

$28 x^{3}$

$42 x^{2}$

$35 x$

$0$

Step 2

Divide the highest order term in the dividend $28 x^{3}$ by the highest order term in divisor $7 x$ .

					$4 x^{2}$
	$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$

Step 3

Multiply the new quotient term by the divisor.

				$4 x^{2}$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			+	$28 x^{3}$	+	$0$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $28 x^{3} + 0$

				$4 x^{2}$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$

Step 5

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

				$4 x^{2}$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$

Step 6

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

				$4 x^{2}$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$

Step 7

Divide the highest order term in the dividend $42 x^{2}$ by the highest order term in divisor $7 x$ .

				$4 x^{2}$	+	$6 x$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$

Step 8

Multiply the new quotient term by the divisor.

				$4 x^{2}$	+	$6 x$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					+	$42 x^{2}$	+	$0$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $42 x^{2} + 0$

				$4 x^{2}$	+	$6 x$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$

Step 10

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

				$4 x^{2}$	+	$6 x$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$

Step 11

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

				$4 x^{2}$	+	$6 x$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$	+	$0$

Step 12

Divide the highest order term in the dividend $- 35 x$ by the highest order term in divisor $7 x$ .

				$4 x^{2}$	+	$6 x$	-	$5$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$	+	$0$

Step 13

Multiply the new quotient term by the divisor.

				$4 x^{2}$	+	$6 x$	-	$5$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$	+	$0$
							-	$35 x$	+	$0$

Step 14

The expression needs to be subtracted from the dividend, so change all the signs in $- 35 x + 0$

				$4 x^{2}$	+	$6 x$	-	$5$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$	+	$0$
							+	$35 x$	-	$0$

Step 15

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

				$4 x^{2}$	+	$6 x$	-	$5$
$7 x$	+	$0$		$28 x^{3}$	+	$42 x^{2}$	-	$35 x$	+	$0$
			-	$28 x^{3}$	-	$0$
					+	$42 x^{2}$	-	$35 x$
					-	$42 x^{2}$	-	$0$
							-	$35 x$	+	$0$
							+	$35 x$	-	$0$
										$0$

Step 16

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

$4 x^{2} + 6 x - 5$