Question

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

Answer 1

`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)`.