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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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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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