How do you factor #22x^2 + 51x - 10#?

1 Answer
Nghi N.
Aug 11, 2015

Factor: #y = 22x^2 + 51x - 10#

Ans: (11x - 2)(2x + 5)

Explanation:

I use the new AC Method. Factored form: y = 22(x + p)(x + q).
Converted trinomial: #y' = x^2 + 51x - 220.# Find 2 numbers p' and q' knowing sum (-51) and product (-220). p' and q' have opposite signs.
Factor pairs of (220) --> ...(-2, 49)(-4, 55). This sum is 51 = b.
Then, p' = -4 and q' = 55.
Therefor: #p = -4/22 = -2/11# and #q = 55/22 = 5/2#

y = 22(x - 2/11)(x + 5/2) = (11x - 2)(2x + 5)

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