SOLUTION: factor the trinomial. m^2 + 4mn - 12n^2

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Question 103798This question is from textbook beginning and intermediate algebra
: factor the trinomial.
m^2 + 4mn - 12n^2
This question is from textbook beginning and intermediate algebra

Found 2 solutions by jim_thompson5910, chriscad:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First think of two numbers that multiply to -12 (the last coefficient) and add to 4 (the second coefficient)


So after going through a list of numbers we get the numbers 6 and -2. These numbers both multiply to -12 and add to 4 (ie -6+2=4 and -6*2=-12)


So now rewrite the expression m%5E2+%2B+4mn+-+12n%5E2 by replacing the 4mn with 6mn-2mn (remember they add to 4)

m%5E2+%2B+6mn+-2mn-+12n%5E2


%28m%5E2+%2B+6mn%29%2B%28+-2mn-+12n%5E2%29 Group like terms


m%28m+%2B+6n%29-2n%28+m%2B+6n%29 Factor out the GCF out of each group


%28m-2n%29%28m+%2B+6n%29 Combine like terms


So m%5E2+%2B+4mn+-+12n%5E2 factors to %28m-2n%29%28m+%2B+6n%29. Notice how %28m-2n%29%28m+%2B+6n%29 foils to m%5E2+%2B+4mn+-+12n%5E2

Answer by chriscad(1) About Me  (Show Source):
You can put this solution on YOUR website!
answer is (m-2n)(m+6n)