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Unformatted text preview: w a must be an integer multiple of 9. Our last concern is end behavior.
Since the leading term of p(x) is ax4 , we need a < 0 to get p(x) → −∞ as x → ±∞. Hence, if we
choose x = −9, we get p(x) = −9x4 + 6x3 − 82x2 + 54x − 9. We can verify our handiwork using
the techniques developed in this chapter. 226 Polynomial Functions This example concludes our study of polynomial functions.9 The last few sections have contained
what is considered by many to be ‘heavy’ mathematics. Like a heavy meal, heavy mathematics
takes time to digest. Don’t be overly concerned if it doesn’t seem to sink in all at once, and pace
yourself on the exercises or you’re liable to get mental cramps. But before we get to the exercises,
we’d like to oﬀer a bit of an epilogue.
Our main goal in presenting the material on the complex zeros of a polynomial was to give the
chapter a sense of completeness. Given that it can be shown that some polynomials have real zeros
which cannot be expressed using the usu...
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