Question

How do you factor the trinomial `7x^2-31x+12`?

Answer 1

(7x - 3)(x - 4)

Explanation:

Use the new AC Method to factor trinomials (Socrtaic Search).
`y = 7x^2 - 31x + 12 =` 7(x + p')(x + q')
Converted trinomial: `y' = x^2 - 31x + 84 =` (x + p')(x + q')
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 84) ---> (2, 42)(3, 28). This sum is (31 = -b).
The opposite sum (-3, -28) give: p' = -3 and q' = -28.
Back to trinomial y: `p = (p')/a = -3/7` and `q = (q')/a = -28/7 = -4`
.
Factored form: `y = 7(x - 3/7)(x - 4) = (7x - 3)(x - 4)`