Question

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

Answer 1

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)`