Find the Quotient of the Two Functions P(x)=x^3-512 , d(x)=x+8

$P (x) = x^{3} - 512$ , $d (x) = x + 8$

Step 1

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

$\frac{x^{3} - 512}{x + 8}$

Step 2

Simplify the numerator.

Rewrite $512$ as $8^{3}$ .

$\frac{x^{3} - 8^{3}}{x + 8}$

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 $b = 8$ .

$\frac{(x - 8) (x^{2} + x \cdot 8 + 8^{2})}{x + 8}$

Simplify.

Move $8$ to the left of $x$ .

$\frac{(x - 8) (x^{2} + 8 \cdot x + 8^{2})}{x + 8}$

Raise $8$ to the power of $2$ .

$\frac{(x - 8) (x^{2} + 8 x + 64)}{x + 8}$

Find the Quotient of the Two Functions P(x)=x^3-512 , d(x)=x+8

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