Find the Quotient of the Two Functions P(x)=x^3-125 d(x)=x+5

$P (x) = x^{3} - 125$ $d (x) = x + 5$

Step 1

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

$\frac{x^{3} - 125}{x + 5}$

Step 2

Simplify the numerator.

Rewrite $125$ as $5^{3}$ .

$\frac{x^{3} - 5^{3}}{x + 5}$

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 $b = 5$ .

$\frac{(x - 5) (x^{2} + x \cdot 5 + 5^{2})}{x + 5}$

Simplify.

Move $5$ to the left of $x$ .

$\frac{(x - 5) (x^{2} + 5 \cdot x + 5^{2})}{x + 5}$

Raise $5$ to the power of $2$ .

$\frac{(x - 5) (x^{2} + 5 x + 25)}{x + 5}$

Find the Quotient of the Two Functions P(x)=x^3-125 d(x)=x+5

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