# How do you factor the expression 2n^2 + 15n + 7?

Dec 3, 2015

Factor y = 2n^2 + 15n + 7

Ans: (2n + 1)(n + 7)

#### Explanation:

y = 2n^2 + 15n + 7 = 2(x + p)(x + q)
I use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial: y' = x^2 + 15n + 14 = (x + p')(x + q').
Factor pairs of (14) --> (1, 14). This sum is (1 + 14 = 15 = b). Then, p' = 1 and q' = 14.
Therefor: p = (p'/a) = 1/ 2 and q = (q')/a = 14/2 = 7.
Factored form: y = 2(n + 1/2)(n + 7) = (2n + 1)(n + 7).