Chapter 2.6, Problem 2E

Solution

To describe: the set of possible rational zeros when using the theorem of the rational zero.

When using the Rational Zero Theorem for $f\left(x\right)=a_n{x}^n+\dots +a_0$ with integer coefficients A list of potential rational roots of the form $\frac{p}{q}$ where $p$ is a factor of $a_0$ and $q$ a

factor of $a_n$ .

The first thing to do to make this list as short as possible, is to make sure the polynomial is simplified. If all $a_k$ have a common factor, divide by it and reduce the list significantly.

Another thing to do is try a few values. If a root $r$ , divide the polynomial

by $x-r$ and get a smaller problem that might be solvable more easily.

With the help of a graphic calculator or another tool, draw the graph and determine which of the root candidates are likely to be true roots and which are more likely to be false roots.