How do you factor #10m^2+7mn-12n^2#?

1 Answer
Nghi N.
May 31, 2015

I use the new AC Method to factor trinomials (Google, Yahoo Search)
y = 10m^2 + 7nm - 12n^2 = (m - p)(m - q).

Convert y to y' = m^2 + 7nm - 120n^2 = (m - p')(m - q')

Compose factor pairs of (a.c = -120n^2) -> (-2, 60)...(-8, 15). (Sum = 7)
Then p' = -8n and q' = 15n.

Then# p = (p')/a = -8n/10 = (-4n)/5#, and #q = (15n)/10 = (3n)/2#

Factored form: #y = (m - (4n)/5)(m + (3n)/2) = (5m - 4n)(2m + 3n)#

Check by developing: #y = (10m^2 + 15nm - 8nm - 12n^2). # OK

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