Question

How do you factor `3y^2+7y-20`?

Answer 1

`f(y) = 3y^2 + 7y - 20`= 3(x - p)(x - q). I use the new AC method

Converted `f'(y) = y^2 + 7y - 60.` a and c have different signs. Compose factor pairs of (a.c = -60) --> (-3, 20)(-4, 15)(-5, 12). This sum is 7 = b. Then p' = -5 and q' = 12.
Back to f(y) -> `p = -5/3 and q = 12/3 = 4.`

Factored form `f(y) = 3(y - 5/3)(y + 4) = (3y - 5)(y + 4).`

Check by developing: `f(y) = 3y^2 + 12 y - 5y - 20.`.OK