Question

How do you factor `3v ^ { 2} - 8v - 60`?

Answer 1

(3v + 10)(v - 6)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`f(x) = 3x^2 - 8x - 60 = 3(x + p)(x + q)`
Converted trinomial `f'(x) = x^2 - 8x - 180 = (x + p')(x + q')`
Find p' and q' knowing they have opposite signs (ac < 0)
Factor pairs of (ac = - 180) -->...(2, -90) ...(10, -18). This last sum is :
-8 = b. Then, p' = 10 and q' = -18.
Back to original y, we have `p = (p')/a = 10/3`, and
`q = (q')/a = -18/3 = - 6.`
Factored form:
`y = 3(x + 10/3)(x - 6) = (3x + 10)(x - 6)`