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**Unformatted text preview: **the list of candidates for rational zeros you obtained in
Example 3.3.2.
3. Use synthetic division to ﬁnd the real zeros of f , and state their multiplicities.
Solution.
1. In Example 3.3.1, we determined all of the real zeros of f lie in the interval [−4, 4]. We set
our window accordingly and get 3.3 Real Zeros of Polynomials 209 2. In Example 3.3.2, we learned that any rational zero of f must be in the list ± 1 , ± 1, ± 3 , ± 3 .
2
2
From the graph, it looks as if we can rule out any of the positive rational zeros, since the
graph seems to cross the x-axis at a value just a little greater than 1. On the negative side,
−1 looks good, so we try that for our synthetic division.
−1 2
4 −1 −6 −3
↓ −2 −2
3
3
2
2 −3 −3 0 We have a winner! Remembering that f was a fourth degree polynomial, we now know our
quotient is a third degree polynomial. If we can do one more successful division, we will have
knocked the quotient down to a quadratic, and, if all else fails, we can use the quadratic
formula to ﬁnd the las...

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