How do you factor this?

12(x+2)^2-14(x+2)-6

1 Answer
Dec 15, 2017

=2(2x+1)(3x+7)

Explanation:

let (x+2)=a for now.

=12a^2-14a-6 Factor out 2
=2(6a^2-7a-3) Factor by grouping - Break middle term
=2(6a^2+2a-9a-3) Factor
=2(2a(3a+1)-3(3a+1)) Factor out (3a+1)
=2(2a-3)(3a+1)

substitute (x+2) for a

=2(2(x+2)-3)(3(x+2)+1) Simplify by distribution
=2(2x+4-3)(3x+6+1) Add/Subtract
=2(2x+1)(3x+7)
Done!

Lets test a value for fun.
for x=1,
=12(1+2)^2-14(1+2)-6
=12(9)-14(3)-6
=108-42-6
=60

Now for the factored version.

=2(2(1)+1)(3(1)+7))
=2(3)(10)
=60

60=60, LS=RS