Algebra Examples

$(3 x^{3} - 3 - 6 x) \div (3 + 3 x)$

Step 1

Move $- 3$ .

$\frac{3 x^{3} - 6 x - 3}{3 + 3 x}$

Step 2

Reorder $3$ and $3 x$ .

$\frac{3 x^{3} - 6 x - 3}{3 x + 3}$

Step 3

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

$3 x$

$3$

$3 x^{3}$

$0 x^{2}$

$6 x$

$3$

Step 4

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

					$x^{2}$
	$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$

Step 5

Multiply the new quotient term by the divisor.

				$x^{2}$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			+	$3 x^{3}$	+	$3 x^{2}$

Step 6

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

				$x^{2}$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$

Step 7

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

				$x^{2}$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$

Step 8

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

				$x^{2}$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$

Step 9

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

				$x^{2}$	-	$x$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$

Step 10

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$x$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					-	$3 x^{2}$	-	$3 x$

Step 11

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

				$x^{2}$	-	$x$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$

Step 12

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

				$x^{2}$	-	$x$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$

Step 13

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

				$x^{2}$	-	$x$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$	-	$3$

Step 14

Divide the highest order term in the dividend $- 3 x$ by the highest order term in divisor $3 x$ .

				$x^{2}$	-	$x$	-	$1$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$	-	$3$

Step 15

Multiply the new quotient term by the divisor.

				$x^{2}$	-	$x$	-	$1$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$	-	$3$
							-	$3 x$	-	$3$

Step 16

The expression needs to be subtracted from the dividend, so change all the signs in $- 3 x - 3$

				$x^{2}$	-	$x$	-	$1$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$	-	$3$
							+	$3 x$	+	$3$

Step 17

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

				$x^{2}$	-	$x$	-	$1$
$3 x$	+	$3$		$3 x^{3}$	+	$0 x^{2}$	-	$6 x$	-	$3$
			-	$3 x^{3}$	-	$3 x^{2}$
					-	$3 x^{2}$	-	$6 x$
					+	$3 x^{2}$	+	$3 x$
							-	$3 x$	-	$3$
							+	$3 x$	+	$3$
										$0$

Step 18

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

$x^{2} - x - 1$