Factor x3 + x2 + x + 1 by grouping. what is the resulting expression?

To factor by grouping, you group up the 1st 2 terms together and the last 2 terms together and then factor those pieces.

(x^3 + x^2) + (x + 1)
x^2(x + 1) + 1(x +1) - now factor out the (x + 1)
(x + 1)(x^2 + 1) - final answer