document.write( "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?
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Algebra.Com's Answer #82463 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Any number that ends in 2 is divisible by 2.
\n" ); document.write( "112=2*56
\n" ); document.write( "I don't think that's what you want to do here.
\n" ); document.write( "I think you want to complete the square.
\n" ); document.write( "That is, there's a number,d, such that
\n" ); document.write( " $\"%28n%2Bd%29%5E2=n%5E2%2B2dn%2Bd%5E2\"$
\n" ); document.write( "If you look at your equation and compare the \"n\" terms, you have
\n" ); document.write( " $\"n%5E2%2B2n+=+n%5E2+%2B2dn\"$
\n" ); document.write( "In your case d=1,
\n" ); document.write( " $\"n%5E2%2B2n+=+%28n%2B1%29%5E2-1\"$
\n" ); document.write( "And then I can substitute in your original equation,
\n" ); document.write( " $\"n%5E2%2B2n-112=0\"$
\n" ); document.write( " $\"%28n%2B1%29%5E2-1-112=0\"$
\n" ); document.write( " $\"%28n%2B1%29%5E2-113=0\"$
\n" ); document.write( " $\"%28n%2B1%29%5E2=113\"$
\n" ); document.write( "The solutions are
\n" ); document.write( " $\"n%2B1=113\"$
\n" ); document.write( " $\"highlight%28n=112%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"n%2B1=-113\"$
\n" ); document.write( " $\"highlight%28n=-114%29\"$ \n" ); document.write( "

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