How do you factor #2x^2 + 11x + 12 #?

1 Answer
May 26, 2016

Answer:

(2x + 3)(x + 4)

Explanation:

Use the new AC Method (Socratic Search)
#y = 2x^2 + 11x + 12 =# 2(x + p)(x + q)
Converted trinomial #y' = x^2 + 11x + 24 =# (x + p')(x + q').
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 24) -->... (3, 8). This sum is 11 = b. Then p' = 3 and q' = 8.
Back to original y,# p = (p')/a = 3/2#, and #q = (q')/a = 8/2 = 4.#
Factored form:# y = 2(x + 3/2)(x + 4) = (2x + 3)(x + 4)#