how to do this math problem?

Question

Factor the polynomial completely.

2x³−24x²+72x

Answer 1

All terms are even and have an x. You can only pull the smallest # of x's.

2x(x²-12x+36)

Now they want you to look at the ()... when i look at the last term (+36) there is a possibility of breaking it apart. I need 2 integers that "add" to -12 and multiply +36...

Because they add to -12... one or both #'s have to be a negative... If one is negative & the other is positive, that will multiply to a negative... but 36 is positive. The only way to multiply to a positive # (+36) is either pos*pos or neg*neg.

It can't be pos*pos... because 2 positives add to a positive and the middle term is (-12).

The only possible answer is  neg and neg. 

 

2x (x-#)(x-#)

 

What are the factors of 36... (1,36) (2,18) (3,12) (4,9) (6,6). There are only 2 numbers that add to 12 and multiply to 36... (6,6). Soooooooo....

 

2x(x-6)(x-6)