How do you factor this?

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

1 Answer
Dylan D.
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#

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