Question

How do you factor `5t^2+37t+42=0`?

Answer 1

(5t + 7)(t + 6)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search)
`y = 5t^2 + 37t + 42 =` 5(t + p)(t + q).
Converted trinomial: `y' = t^2 + 37t + 210 =` (t + p')(t + q').
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 210) -->...(5, 42)(6, 35)(7, 30). This sum is (37 = b). Then, p' = 7 and q' = 30.
Back to original trinomial y --> `p = (p')/a = 7/5` and `q = (q')/a = 30/5 = 6`
Factored form: y = 5(t + 7/5)(x + 6) = (5t + 7)(t + 6).