Question

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

Answer 1

`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`