Divide (x^3-1331)/(x-11)

$\frac{x^{3} - 1331}{x - 11}$

Step 1

Simplify the numerator.

Rewrite $1331$ as $11^{3}$ .

$\frac{x^{3} - 11^{3}}{x - 11}$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 11$ .

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

Simplify.

Move $11$ to the left of $x$ .

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

Raise $11$ to the power of $2$ .

$\frac{(x - 11) (x^{2} + 11 x + 121)}{x - 11}$

Step 2

Cancel the common factor of $x - 11$ .

Cancel the common factor.

$\frac{(x - 11) (x^{2} + 11 x + 121)}{x - 11}$

Divide $x^{2} + 11 x + 121$ by $1$ .

$x^{2} + 11 x + 121$

Divide (x^3-1331)/(x-11)

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