Divide (2x^3-3x^2+4x-7)/(x^2+3)

$\frac{2 x^{3} - 3 x^{2} + 4 x - 7}{x^{2} + 3}$

Step 1

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

$x^{2}$

$0 x$

$3$

$2 x^{3}$

$3 x^{2}$

$4 x$

$7$

Step 2

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

$2 x$

$x^{2}$

$0 x$

$3$

$2 x^{3}$

$3 x^{2}$

$4 x$

$7$

Step 3

Multiply the new quotient term by the divisor.

$2 x$

$x^{2}$

$0 x$

$3$

$2 x^{3}$

$3 x^{2}$

$4 x$

$7$

$2 x^{3}$

$0$

$6 x$

Step 4

The expression needs to be subtracted from the dividend, so change all the signs in $2 x^{3} + 0 + 6 x$

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

Step 5

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

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

Step 6

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

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

Step 7

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

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

Step 8

Multiply the new quotient term by the divisor.

						$2 x$	-	$3$
$x^{2}$	+	$0 x$	+	$3$		$2 x^{3}$	-	$3 x^{2}$	+	$4 x$	-	$7$
					-	$2 x^{3}$	-	$0$	-	$6 x$
							-	$3 x^{2}$	-	$2 x$	-	$7$
							-	$3 x^{2}$	+	$0$	-	$9$

Step 9

The expression needs to be subtracted from the dividend, so change all the signs in $- 3 x^{2} + 0 - 9$

						$2 x$	-	$3$
$x^{2}$	+	$0 x$	+	$3$		$2 x^{3}$	-	$3 x^{2}$	+	$4 x$	-	$7$
					-	$2 x^{3}$	-	$0$	-	$6 x$
							-	$3 x^{2}$	-	$2 x$	-	$7$
							+	$3 x^{2}$	-	$0$	+	$9$

Step 10

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

						$2 x$	-	$3$
$x^{2}$	+	$0 x$	+	$3$		$2 x^{3}$	-	$3 x^{2}$	+	$4 x$	-	$7$
					-	$2 x^{3}$	-	$0$	-	$6 x$
							-	$3 x^{2}$	-	$2 x$	-	$7$
							+	$3 x^{2}$	-	$0$	+	$9$
									-	$2 x$	+	$2$

Step 11

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

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

Divide (2x^3-3x^2+4x-7)/(x^2+3)

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