Answer
$f(-3)$ and $f(-2)$ have opposite signs,
so f(x) has a real zero between $-3$ and $-2$
Work Step by Step
The Intermediate Value Theorem for Polynomial Functions$:$
Let $f$ be a polynomial function with real coefficients.
If $f(a)$ and $f(b)$ have opposite signs,
then there is at least one value of $c$ between $a$ and $b$ for which $f(c)=0$.
-------------------
$ a=-3,\quad f(a)=(-3)^{3}+(-3)^{2}-2(-3)+1=-27+9+6+1=-11\quad$(negative)
$ b=-2,\quad f(b)=(-2)^{3}+(-2)^{2}-2(-2)+1=-8+4+4+1=1\quad$(positive)
$f(-3)$ and $f(-2)$ have opposite signs,
so f(x) has a real zero between $-3$ and $-2$
