How do you factor completely #6x^2-2x-20#?

1 Answer
Jun 10, 2016

Answer:

2(3x + 5)(x - 2)

Explanation:

#f(x) = 2y = 2(3x^2 - x - 10).#
Factor the trinomial y, in parentheses, by the new AC method (Socratic Search).
#y = 3x^2 - x - 10 =# 3(x + p)(x + q)
Converted trinomial: #y' = x^2 - x - 30 =# (x + p')(x + q')
Find p' and q', knowing their sum (-1) and their product (-30).
They are: p' = 5 and q' = -6.
Back to y, --> #p = (p')/a = 5/3# and #q = (q')/a = -6/3 = -2#.
Factored form: #y = 3(x + 5/3)(x - 2) = (3x + 5)(x - 2)#
Finally,
#f(x) = 2(3x + 5)(x - 2)#