How do you factor #5x^2-16x+12#?

1 Answer
Jun 27, 2015

Answer:

#5x^2-16x+12 = (5x-6)((x-2)#

Explanation:

Hoping for rational factors, we note that
the only factors of #5# are #(1,5)#

So we are looking for values #a# and #b#
#color(white)("XXXX")##(1x-a)(5x-b) = 5x^2 - (5a+b)x +ab#
such that #a*b = 12#
and #5a+b = 16#

The #(a,b)# factors of 12 are #(1,12), (2,6), (3,4), (4,3), (6,2), (12,1)#

We can check each pair for a pair that satisfies #5a+b = 16#
until we find #(a,b)=(2,6)#
which implies our factors are
#color(white)("XXXX")##(x-2)(5x-6)#