Answer
$(x+1)(x^2+2)$.
Work Step by Step
The given polynomial is
$= x^3+x^2+2x+2$
Group the terms.
$= (x^3+x^2)+(2x+2)$
Factor each group.
$= x^2(x+1)+2(x+1)$
Factor out $(x+1)$.
$= (x+1)(x^2+2)$
Hence, the complete factor of the polynomial is $(x+1)(x^2+2)$.
