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
Factoring Question
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Hi Woodencrawdad!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
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
Whitney Garner
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
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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 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.
GMAT/MBA Expert
- Whitney Garner
- GMAT Instructor
- Posts: 273
- Joined: Tue Sep 21, 2010 5:37 am
- Location: Raleigh, NC
- Thanked: 154 times
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- GMAT Score:770
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!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.
Good luck with your Studies!!
Whit
Whitney Garner
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated
GMAT Instructor & Instructor Developer
Manhattan Prep
Contributor to Beat The GMAT!
Math is a lot like love - a simple idea that can easily get complicated