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

Dec 2, 2015

Answer:

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

Ans:$- \left(8 t - 7\right) \left(2 t + 13\right)$

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
$y = - \left(16 {t}^{2} + 90 t - 91\right) =$ -16(x + p)(x + q)
Converted trinomial $y ' = - \left({t}^{2} + 90 t - 1456\right) =$ -(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, $p = \frac{p '}{a} = - \frac{14}{16} = - \frac{7}{8}$ and $q = \frac{q '}{a} = \frac{104}{16} = \frac{13}{2}$.
Factored form: $y = - 16 \left(t - \frac{7}{8}\right) \left(t + \frac{13}{2}\right) = - \left(8 t - 7\right) \left(2 t + 13\right) .$

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