Pre-Algebra Examples

$\frac{11^{3} + 11 x - 38}{x + 2}$

Step 1

Expand $11^{3} + 11 x - 38$ .

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Step 1.1

Rewrite the exponentiation as a product.

$\frac{11 \cdot 11^{2} + 11 x - 38}{x + 2}$

Step 1.2

Rewrite the exponentiation as a product.

$\frac{11 \cdot (11 \cdot 11) + 11 x - 38}{x + 2}$

Step 1.3

Remove parentheses.

$\frac{11 \cdot 11 \cdot 11 + 11 x - 38}{x + 2}$

Step 1.4

Multiply $11$ by $11$ .

$\frac{121 \cdot 11 + 11 x - 38}{x + 2}$

Step 1.5

Multiply $121$ by $11$ .

$\frac{1331 + 11 x - 38}{x + 2}$

Step 1.6

Reorder $1331$ and $11 x$ .

$\frac{11 x + 1331 - 38}{x + 2}$

Step 1.7

Subtract $38$ from $1331$ .

$\frac{11 x + 1293}{x + 2}$

Step 2

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

$x$

$2$

$11 x$

$1293$

Step 3

Divide the highest order term in the dividend $11 x$ by the highest order term in divisor $x$ .

					$11$
	$x$	+	$2$		$11 x$	+	$1293$

Step 4

Multiply the new quotient term by the divisor.

Step 5

The expression needs to be subtracted from the dividend, so change all the signs in $11 x + 22$

Step 6

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

Step 7

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

$11 + \frac{1271}{x + 2}$