Answer
(a) see explanations.
(b) see explanations.
Work Step by Step
(a) Use synthetic division, divide $f(x)$ by $x-1$ as shown in the figure (top half). We can see that all numbers in the bottom row of the division are nonnegative. Based on the Boundedness theorem, $f(x)$ has no zero greater than $1$.
(b) Similarly, divide $f(x)$ by $x+3$ as shown in the figure (lower half). We can see that the numbers in the bottom row of the division alternate in sign. Based on the Boundedness theorem, $f(x)$ has no zero less than $-3$.