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

Answer 1

Abigail Allen

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

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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Answer 2

Hazel Anglin

To factor the trinomial 100x^3 - 40x^2 + 4x, you can first factor out the greatest common factor, which is 4x. This leaves you with 4x(25x^2 - 10x + 1). Then, you can factor the quadratic expression inside the parentheses using techniques such as factoring by grouping or the quadratic formula. In this case, the quadratic factors to (5x - 1)(5x - 1). So, the factored form of the trinomial is 4x(5x - 1)^2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.