How do you factor by grouping #t^3 + 6t^2 - 2t - 12#?

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Answer 1 · 2015-04-28T23:03:42

Group #t^3 # and 6t^2 # like this,

#t^2(t+6)#

then group #-2t # and #-12 # like this,

#-2(t+6)#

Now add the two,

#t^2(t+6)-2(t+6) => (t^2-2)(t+6)#

Now, further #t^2-2# is a difference of two squares so you factorize thus,

#t^2-2=(t-sqrt(2))(t+sqrt(2))#

So, the final result is #(t-sqrt(2))(t+sqrt(2))(t+6)#