# How do you factor 2t²-3t-20?

Nov 18, 2015

Factor $y = 2 {t}^{2} - 3 t - 20.$

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

#### Explanation:

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