# How do you factor 10t^(2) - 43t + 12?

Jun 30, 2016

(10t - 3)(t - 4)

#### Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
$y = 10 {t}^{2} - 43 t + 12 =$ 10(t + p)(t + q)
Converted trinomial:$y ' = {t}^{2} - 43 t + 120 =$ (t + p')(t + q').
Find p' and q', that have same sign (ac > 0), and that have as sum (b = -43) and as product (ac = 120).
Factor pairs of (120) --> (3, 40)(-3, -40). This sum is (-43 = b). Then p' = -3 and q' = -40.
Back to original y, $p = \frac{p '}{a} = - \frac{3}{10}$, and $q = \frac{q '}{a} = - \frac{40}{10} = - 4$.
Factored form: $y = 10 \left(t - \frac{3}{10}\right) \left(t - 4\right) = \left(10 t - 3\right) \left(t - 4\right)$