Question

How do you factor the trinomial `-20a^3+15a+13a^2`?

Answer 1

-a(5a + 3)(4a - 5)

Explanation:

`f(a) = -ay= - a(20a^2 - 13a - 15).` Factor the trinomial y.
Use the new AC Method (Socratic Search)
`y = 20a^2 - 13a - 15 =`20(a + p)(a + q)
Converted trinomial: `y' = a^2 - 13a - 300 =` (a + p')(a + q').
p' and q, have opposite signs because ac < 0.
Factor pairs of (ac = -300) -->... (-10, 30)(10, -30)(-12, 25)(12, -25). This last sum is (-13 = -b). Then p' = 12 and q' = -25.
Back to y, `p = (p')/a = 12/20 = 3/5` and `q = (q')/a = -25/20 = -5/4`
Therefor,
`y = 20(a + 3/5)(a - 5/4) = (5a + 3)(4a - 5).`
Finally,
`f(a) = -ay = -a(5a + 3)(4a - 5)`