3. Find all rational roots of the polynomials:

a) $x^{4}-3 x^{3}-8 x^{2}+12 x+16$

b) $8 x^{3}-20 x^{2}-2 x+5$

c) $4 x^{4}-16 x^{3}+11 x^{2}+4 x-3$.
$\triangle$ a) The polynomial is monic, so by Theorem 7, all its rational roots are integers. We find them using the familiar method; we get the roots $-1, 2, -2, 4$.

b) Consider the equation

$$
8 x^{3}-20 x^{2}-2 x+5=0
$$

We make the polynomial on its left side monic. For this, let $2 x=y$. We will have:

$$
y^{3}-5 y^{2}-y+5=0
$$

We find the integer roots of the last equation: $y_{1,2}= \pm 1, y_{3}=5$. From this, the roots of the original polynomial are $x_{1,2}= \pm 1 / 2, x_{3}=5 / 2$.

c) Consider the equation

$$
4 x^{4}-16 x^{3}+11 x^{2}+4 x-3=0
$$

First, multiply it by 4, and then introduce the substitution $2 x=y$:

$$
y^{4}-8 y^{3}+11 y^{2}+8 y-12=0
$$

The roots of the last equation are $-y_{1,2}= \pm 1, y_{3}=2, y_{4}=6$. Then the roots of the original polynomial are $-x_{1,2}= \pm 1 / 2, x_{3}=1, x_{4}=3$.

Answer: a) $-1, \pm 2, 4$; b) $\pm 1 / 2, 5 / 2$; c) $\pm 1 / 2, 1, 3$.