Question

How do you factor by grouping `t^3+2t^2-7t-14`?

Answer 1

`t^3 + 2t^2 - 7t - 14 = (t^3 + 2t^2) - (7t + 14)`
`= t^2(t + 2) - 7(t + 2) = (t^2 - 7)(t + 2)`

So grouping the first two terms together and the last two terms together allows us to notice the common factor `(t + 2)`.

If we allow irrational coefficients, `(t^2 - 7)` factors as `(t - sqrt(7))(t + sqrt(7))`.