Divide Divide 3x^3-3x^2-4x+3 by x+3

Divide $3 x^{3} - 3 x^{2} - 4 x + 3$ by $x + 3$

Step 1

Write the problem as a mathematical expression.

Divide $\frac{3 x^{3} - 3 x^{2} - 4 x + 3}{x + 3}$

Step 2

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

$x$

$3$

$3 x^{3}$

$3 x^{2}$

$4 x$

$3$

Step 3

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

					$3 x^{2}$
	$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$

Step 4

Multiply the new quotient term by the divisor.

				$3 x^{2}$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			+	$3 x^{3}$	+	$9 x^{2}$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $3 x^{3} + 9 x^{2}$

				$3 x^{2}$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$

Step 6

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

				$3 x^{2}$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$

Step 7

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

				$3 x^{2}$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$

Step 8

Divide the highest order term in the dividend $- 12 x^{2}$ by the highest order term in divisor $x$ .

				$3 x^{2}$	-	$12 x$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$

Step 9

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$12 x$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					-	$12 x^{2}$	-	$36 x$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 12 x^{2} - 36 x$

				$3 x^{2}$	-	$12 x$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$

Step 11

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

				$3 x^{2}$	-	$12 x$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$

Step 12

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

				$3 x^{2}$	-	$12 x$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$	+	$3$

Step 13

Divide the highest order term in the dividend $32 x$ by the highest order term in divisor $x$ .

				$3 x^{2}$	-	$12 x$	+	$32$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$	+	$3$

Step 14

Multiply the new quotient term by the divisor.

				$3 x^{2}$	-	$12 x$	+	$32$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$	+	$3$
							+	$32 x$	+	$96$

Step 15

The expression needs to be subtracted from the dividend, so change all the signs in $32 x + 96$

				$3 x^{2}$	-	$12 x$	+	$32$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$	+	$3$
							-	$32 x$	-	$96$

Step 16

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

				$3 x^{2}$	-	$12 x$	+	$32$
$x$	+	$3$		$3 x^{3}$	-	$3 x^{2}$	-	$4 x$	+	$3$
			-	$3 x^{3}$	-	$9 x^{2}$
					-	$12 x^{2}$	-	$4 x$
					+	$12 x^{2}$	+	$36 x$
							+	$32 x$	+	$3$
							-	$32 x$	-	$96$
									-	$93$

Step 17

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

$3 x^{2} - 12 x + 32 - \frac{93}{x + 3}$

Divide Divide 3x^3-3x^2-4x+3 by x+3

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