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

1 Answer
Nghi N.
Jun 30, 2016

(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)#

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