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**Unformatted text preview: **ant term, a0 = −3, and divide them by each of the factors of the leading coeﬃcient a4 = 2.
The factors of −3 are ± 1 and ± 3. Since the Rational Zeros Theorem tacks on a ± anyway, for
the moment, we consider only the positive factors 1 and 3. The factors of 2 are 1 and 2, so the
3
Rational Zeros Theorem gives the list ± 1 , ± 1 , ± 3 , ± 2 or ± 1 , ± 1, ± 3 , ± 3 .
1
2
1
2
2
Our discussion now diverges between those who wish to use technology and those who do not. 3.3.1 For Those Wishing to use a Graphing Calculator At this stage, we know not only the interval in which all of the zeros of f (x) = 2x4 +4x3 − x2 − 6x − 3
are located, but we also know some potential candidates. We can now use our calculator to help
us determine all of the real zeros of f , as illustrated in the next example.
Example 3.3.3. Let f (x) = 2x4 + 4x3 − x2 − 6x − 3.
1. Graph y = f (x) on the calculator using the interval obtained in Example 3.3.1 as a guide.
2. Use the graph to help narrow down...

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