Answered: 1. The polynomial P(x) = 5x^2(x −…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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1. The polynomial P(x) = 5x^2(x − 1)^3(x + 8) has degree _______ It has zeros 0, 1, and _________ The zero 0 has multiplicity _____ , and the zero 1 has multiplicity ______. 2. True or False? If False, give a reason. Let P(x) = x^4 + 1. (a) The polynomial P has four complex zeros. True False; P has degree 5, so by the Zeros Theorem it has five (not necessarily distinct) complex zeros. False; the only zero of P(x) is x = 1. False; P has no zeros. False; the only zero of P(x) is x = −1. (b) The polynomial P can be factored into linear factors with complex coefficients. True False; coefficients can't be complex. False; by the Zeros Theorem. False; P cannot be factored. False; by the Complete Factorization Theorem. (c) Some of the zeros of P are real. True False; P has no zeros. False; zeros of 4th degree polynomials can't be real. False; by the Fundamental Theorem of Algebra. False; the fourth power of any real number is nonnegative, so P(x) ≥ 1 for all real x and P has no real zeros. 3) A polynomial P is given. P(x) = x^4 + 32x^2 + 256 (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) x = (b) Factor P completely. P(x) =

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