Stitz-Zeager_College_Algebra_e-book

# However it is dicult to see what is happening near x

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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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