How do you factor #3x^2 + 5x - 28#?

2 Answers
Apr 21, 2016

Answer:

#3x^2+5x-28=(3x-7)(x+4)#

Explanation:

#3x^2+5x-28=(3x-7)(x+4)#

Apr 21, 2016

Answer:

(3x - 7)(x + 4)

Explanation:

Use the new AC method to factor trinomials (Socratic Search)
#y = 3x^2 + 5x - 28 =# 3(x + p)(x + q)
#Converted trinomial y' = x^2 + 5x - 84 =# (x + p')(x + q')
p' and q' have opposite signs, because ac < 0.
Factor pairs of (ac = -84) -->...(-4, 21)(-7, 12). This sum is 5 = b. Then, p' = -7 and q' = 12.
Back to y, #p = (p')/a = -7/3# and #q = (q')/a = 12/3 = 4.#
Factored form:
#y = 3(x - 7/3)(x + 4) = (3x - 7)(x + 4)#