Question

How do you factor by grouping `t^3-t^2+t-1`?

Answer 1

`t^3-t^2+t-1 = (t^3-t^2)+(t-1)`
`= t^2(t-1)+1(t-1)=(t^2+1)(t-1)`.

Since `t^2+1 > 0` for all real values of `t`, there are no smaller factors with real coefficients.