Consider the following. f(x) = x4 − 3x3 − 4x2 − 12x − 32 (a) Write the polynomial as the product of factors that are irreducible over the rationals. (Hint: One factor is x2 + 4.) f(x) = (b) Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. f(x) = (c) Write the polynomial in completely factored form. f(x) =

Consider the following. f(x) = x4 − 3x3 − 4x2 − 12x − 32 (a) Write the polynomial as the product of factors that are irreducible over the rationals. (Hint: One factor is x2 + 4.) f(x) = (b) Write the polynomial as the product of linear and quadratic factors that are irreducible over the reals. f(x) = (c) Write the polynomial in completely factored form. f(x) =

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section: Chapter Questions

Problem 8T: Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result...

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Find the difference2x3x+3x22x3 and write the resulting polynomial in standard form.
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Find all real solutions of 2x35x2+15x+18=0.
Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result to factor the polynomial function completely and list all the zeros of the function.
What does it mean to say a polynomial is in factored form?