Q. 455 - Intermediate Algebra

Question

In the following exercises, factor completely.

$x^3+125$

Step-by-Step Solution

Answer

On factoring, we get $\left(x+5\right)\left(x^2-5x+25\right)$.

Step 1. Given information.

Consider the given question,

$x^3+125$

Write using the sum of cubes pattern,

$=x^3+5^3$

Factor out,

$=\left(x+5\right)\left(x^2-5x+25\right)$

Step 2. Check the answers.

Check by multiplying,

$$\begin{gathered} =\left(x+5\right)\left(x^2-5x+25\right) \\ =x^3-5x^2+25x+5x^2-25x-125 \\ =x^3-125 \end{gathered}$$

This is true.