How do you factor the trinomial #16b^2 +10b -21 #?

1 Answer
Nghi N.
Feb 24, 2016

y = (8x - 7)(2x + 3)

Explanation:

I use the systematic new AC Method to factor trinomials (Socratic Search)
#y = 16x^2 + 10x - 21 =# 16(x + p)(x + q)
Converted trinomial: #y' = x^2 + 10x - 336 = #16(x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Compose factor pairs of (ac = - 336) --> ...(-12, 28)(-14, 24). This sum
is (24 - 14 = 10 = b). Then p' = -14 and q' = 24.
Back to original trinomial:# p = (p')/a = -14/16 = -7/8# and #q = (q')/a = 24/ 16 = 3/2#.
Factored form:# y = 16(x - 7/8)(x + 3/2) = (8x - 7)(2x + 3)#

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