How do you factor #10x^2 - 7x - 12#?
Use a variant of the AC Method.
Look for a pair of factors of
Now use that pair to split the middle term, then factor by grouping...
The method George used is the popular factoring AC Method (YouTube). To avoid the lengthy factoring by grouping, you may use the new AC Method.
Convert y to
Find p' and q' by composing factor pairs of (a.c = -120). a and c have different signs. Proceed: ...(-4, 30)(-5, 24)(-8, 15). This sum is 7 = -b. Then p' = 8 and q' = -15.
Check by developing: f(x) = 10x^2 - 15x + 8x - 12. OK.
This new AC Method is fast, systematic, no guessing, no factoring by grouping.