Question

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

Answer 1

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