Question

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

Answer 1

(10t - 3)(t - 4)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`y = 10t^2 - 43t + 12 =` 10(t + p)(t + q)
Converted trinomial:`y' = t^2 - 43t + 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 = (p')/a = -3/10`, and `q = (q')/a = -40/10 = -4`.
Factored form: `y = 10(t -3/10)(t - 4) = (10t -3)(t - 4)`