How do you factor completely #2x^3 -32x#?

1 Answer
Nov 15, 2015

Answer:

#2x(x+4)(x-4)#

Explanation:

Look for a common factor between the two terms. If you focus on just the constants, #2# and #32#, it is clear that their greatest common factor is #2#.
So, we can "take a #2#" out of both terms in #2x^3-32x#.
We can rewrite it as #2(x^3-16x)#.
We can also factor out an #x# from both terms: #2x(x^2-16)#
We are not done. The term #x^2-16# is a "difference of squares".
Differences of squares, like #a^2-b^2#, can be factored into #(a+b)(a-b)#.
Therefore, we can factor #x^2-16# into #(x+4)(x-4)#.

So, we can factor the entire term into #2x(x+4)(x-4)#.