Question

How do you factor `2t²-3t-20`?

Answer 1

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)`