How do you factor #4x^2+17x-15#?

1 Answer
Nghi N.
Aug 5, 2015

Factor: y = 4x^2 + 17x - 15 (1)

Ans: (4x - 3)(x + 5)

Explanation:

y = 4(x - p)(x - q)
I use the new AC method to factor trinomials.
Converted trinomial: #y' = x^2 + 17x - 60#= (x - p')(x - q')
p' and q' have opposite sign.
Factor pairs of -60 -->( -2, 30)(-3, 20). This sum is 17 = b.
Then p' = -3 and q' = 20
Therefor, #p = (p')/a = -3/4#, and #q' = 20/4 = 5#

#y = 4(x - 3/4)(x + 5) = (4x - 3)(x + 5)#

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