1. Find all integer roots of the polynomial:

$$
f(x)=4 x^{4}-16 x^{3}+11 x^{2}+4 x-3
$$
$\triangle$ By Theorem 6, all integer roots of the given polynomial are among the divisors of the constant term, i.e., among the numbers $\pm 1, \pm 3$.

Let's check if $x=1$ is a root of the polynomial. We will have:

$$
f(1)=4-16+11+4-3=0
$$

Therefore, $x=1$ is a root of the polynomial.

For $x=-1, x=3$, and $x=-3$, we get:

$f(-1)=4+16+11-4-3>0$

$f(3)=324-432+99+12-3=0$,

$f(-3)=324+432+99-12-3>0$.

Of these three values of $x$, only $x=3$ turned out to be a root of the polynomial.

Answer: $1,3$.