How do you factor the trinomial 100x^3-40x^2+4x?

1 Answer
Apr 30, 2016

100x^3-40x^2+4x = 4x(5x-1)^2

Explanation:

All of the terms are divisible by 4x, so separate that out as a factor first.

100x^3-40x^2+4x

=4x(25x^2-10x+1)

The remaining quadratic factor is a perfect square trinomial:

25x^2-10x+1 = (5x)^2-2(5x)+1^2 = (5x-1)^2

So:

100x^3-40x^2+4x = 4x(5x-1)^2