Algebra Examples

$(x^{3} + 43 - 49 x - 7 x^{2}) \div (x^{2} - 49)$

Step 1

Expand $x^{3} + 43 - 49 x - 7 x^{2}$ .

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Step 1.1

Move $43$ .

$\frac{x^{3} - 49 x + 43 - 7 x^{2}}{x^{2} - 49}$

Step 1.2

Move $43$ .

$\frac{x^{3} - 49 x - 7 x^{2} + 43}{x^{2} - 49}$

Step 1.3

Move $- 49 x$ .

$\frac{x^{3} - 7 x^{2} - 49 x + 43}{x^{2} - 49}$

Step 2

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

$x^{2}$

$0 x$

$49$

$x^{3}$

$7 x^{2}$

$49 x$

$43$

Step 3

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

$x$

$x^{2}$

$0 x$

$49$

$x^{3}$

$7 x^{2}$

$49 x$

$43$

Step 4

Multiply the new quotient term by the divisor.

$x$

$x^{2}$

$0 x$

$49$

$x^{3}$

$7 x^{2}$

$49 x$

$43$

$x^{3}$

$0$

$49 x$

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $x^{3} + 0 - 49 x$

						$x$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$

Step 6

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

						$x$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$

Step 7

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

						$x$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$	+	$43$

Step 8

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

						$x$	-	$7$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$	+	$43$

Step 9

Multiply the new quotient term by the divisor.

						$x$	-	$7$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$	+	$43$
							-	$7 x^{2}$	+	$0$	+	$343$

Step 10

The expression needs to be subtracted from the dividend, so change all the signs in $- 7 x^{2} + 0 + 343$

						$x$	-	$7$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$	+	$43$
							+	$7 x^{2}$	-	$0$	-	$343$

Step 11

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

						$x$	-	$7$
$x^{2}$	+	$0 x$	-	$49$		$x^{3}$	-	$7 x^{2}$	-	$49 x$	+	$43$
					-	$x^{3}$	-	$0$	+	$49 x$
							-	$7 x^{2}$	+	$0$	+	$43$
							+	$7 x^{2}$	-	$0$	-	$343$
											-	$300$

Step 12

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

$x - 7 - \frac{300}{x^{2} - 49}$