Factoring Question

Woodencrawdad wrote:Can someone explain how you simplify #1 to #2? Can't seem to see how they arrived at the simplification in #2.

1) x(x-1)^2 + 5(x-1)^2 = 0

2) (x+5)(x-1)^2 = 0

Hi Woodencrawdad!

This factorization might be a bit difficult to see right away, so I would recommend using a "substitution" trick that I sometimes find handy! Notice that both terms in #1 have an (x-1)^2 term. Let's use a simple substitution variable to put in this place, so why don't we say that H = (x-1)^2.

Now #1 becomes:
x(H) + 5(H) = 0

Since both terms have an H, we can factor it out!

H(x+5) = 0
or
(x+5)(H) = 0

And now, we just replace our H with what it was originally

(x+5)(x-1)^2 = 0

And then, since this product =0, then one piece must =0 for it to be true and we can solve as we would any other quadratic:

x+5=0, or (x-1)^2=0
x = -5, or x-1=0 --> x=1

So the solutions for this equation are x=-5, 1


Whit

Woodencrawdad wrote:Whitney,

I seriously appreciate this. I was over-thinking it and your solution helped me see a simple way of solving. Thanks very much! By the way, I'm using Manhattan products for prep and really benefiting.

I'm so glad to hear it helped!! I know that for me, a lot of the challenge comes from how scary or overwhelming a problem can "LOOK" and so I do just as you said... over-complicate things and get stuck!! So I'm always trying to remind myself to look for the "easy" GMAT problem that is hiding behind this big, tough exterior!

Good luck with your Studies!!

Whit