Calculus Examples

$P (x) = x^{3} - 216$ $D (x) = x + 6$

Step 1

Replace the function designators with the actual functions in $\frac{P (x)}{D (x)}$ .

$\frac{x^{3} - 216}{x + 6}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $216$ as $6^{3}$ .

$\frac{x^{3} - 6^{3}}{x + 6}$

Step 2.2

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 $b = 6$ .

$\frac{(x - 6) (x^{2} + x \cdot 6 + 6^{2})}{x + 6}$

Step 2.3

Simplify.

Tap for more steps...

Step 2.3.1

Move $6$ to the left of $x$ .

$\frac{(x - 6) (x^{2} + 6 \cdot x + 6^{2})}{x + 6}$

Step 2.3.2

Raise $6$ to the power of $2$ .

$\frac{(x - 6) (x^{2} + 6 x + 36)}{x + 6}$