How do you factor #2t²-3t-20#?

1 Answer
Nov 18, 2015

Answer:

Factor #y = 2t^2 - 3t - 20.#

Ans: y = (2t + 5)(t - 4)

Explanation:

I use the new AC Method (Socratic Search)
#y = 2t^2 - 3t - 20 =# 2(x + p)(x + q)
Converted #y' = t^2 - 3t - 40.# = (t + p')(t + q')
Factor pairs of (-40) --> (-4, 10)(-5, 8). This sum is 3 = -b. Then p' = 5 and q' = -8.
Therefor, #p = 5/2# and #q = -8/2 = -4.#
Factored form: #y = 2(t + 5/2)(t - 4) = (2t + 5)(t - 4)#