Chapter 8.5, Problem 28PPS

To determine

The factorization of the polynomial.

Answer to Problem 28PPS

  $5a\left(a-2\right)\left(a+2\right)$

Explanation of Solution

Given:

The given polynomial is:

  $5a^3-20a$

Calculation:

It is known that,

  $a^2-b^2=\left(a+b\right)\left(a-b\right)$

The given polynomial can be written as:

  $\begin{array}{l}=5a^3-20a\\ =5a\left(a^2-4\right)\\ =5a\left({\left(a\right)}^2-{\left(2\right)}^2\right)\\ =5a\left(a-2\right)\left(a+2\right)\end{array}$