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

May 9, 2016

(5t + 7)(t + 6)

#### Explanation:

Use the new AC Method to factor trinomials (Socratic Search)
$y = 5 {t}^{2} + 37 t + 42 =$ 5(t + p)(t + q).
Converted trinomial: $y ' = {t}^{2} + 37 t + 210 =$ (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 --> $p = \frac{p '}{a} = \frac{7}{5}$ and $q = \frac{q '}{a} = \frac{30}{5} = 6$
Factored form: y = 5(t + 7/5)(x + 6) = (5t + 7)(t + 6).