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

1 Answer
Nghi N.
Dec 2, 2015

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.

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