Question

How do you factor the expression `91-90t-16t^2`?

Answer 1

Factor y = -16t^2 - 90t + 91

Ans:`-(8t - 7)(2t + 13)`

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`y = -(16t^2 + 90t - 91) =` -16(x + p)(x + q)
Converted trinomial `y' = -(t^2 + 90 t - 1456) =` -(t + p')(t + q').
p' and q' have opposite signs.
Factor pairs of (-1456) --> ...(-8, 182)(-14, 104). This sum is (- 14 + 104) = 90 = b. Then, p' = -14 and q' = 104.
Therefor, `p = (p')/a = -14/16 = -7/8` and `q = (q')/a = 104/16 = 13/2`.
Factored form: `y = -16(t - 7/8)(t + 13/2) = -(8t - 7)(2t + 13).`

NOTE. This method is systematic. There are no guessing and no lengthy factoring by grouping.