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

1 Answer
George C.
Apr 21, 2016

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))

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