Question

How do you factor `2x^3 - 4x`?

Answer 1

`2x^3-4x = 2x(x-sqrt(2))(x+sqrt(2))`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

We use this with `a=x` and `b=sqrt(2)` later.

`color(white)()`
First note that both terms are divisible by `2` and by `x`, so they are both divisible by `2x`, so separate that out as a factor first...

`2x^3-4x = 2x(x^2-2) = 2x(x^2-(sqrt(2))^2) = 2x(x-sqrt(2))(x+sqrt(2))`