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

1 Answer
George C.
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#

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