SOLUTION: I'm trying to factor polynomials; I'm doing word problems. However, I cannot understand how to find the factor of a number that will add up to the middle number. For example n^2+

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm trying to factor polynomials; I'm doing word problems. However, I cannot understand how to find the factor of a number that will add up to the middle number. For example n^2+      Log On


   

Question 113317: I'm trying to factor polynomials; I'm doing word problems. However, I cannot understand how to find the factor of a number that will add up to the middle number. For example n^2+2n-112=0 - 2(n2+n-112)= 0 - (n )(n ) How do I find the multiples for 112. Is there an easy method?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Any number that ends in 2 is divisible by 2.
112=2*56
I don't think that's what you want to do here.
I think you want to complete the square.
That is, there's a number,d, such that
%28n%2Bd%29%5E2=n%5E2%2B2dn%2Bd%5E2
If you look at your equation and compare the "n" terms, you have
n%5E2%2B2n+=+n%5E2+%2B2dn
In your case d=1,
n%5E2%2B2n+=+%28n%2B1%29%5E2-1
And then I can substitute in your original equation,
n%5E2%2B2n-112=0
%28n%2B1%29%5E2-1-112=0
%28n%2B1%29%5E2-113=0
%28n%2B1%29%5E2=113
The solutions are
n%2B1=113
highlight%28n=112%29
and
n%2B1=-113
highlight%28n=-114%29