True or False Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors. (p. 219)
True or False Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors. (p. 219)
Solution Summary: The author explains that every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors.
True or False Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors. (p. 219)
Expert Solution & Answer
To determine
True or False.
Answer to Problem 4AYU
Solution:
True.
Explanation of Solution
Given:
Every polynomial with real numbers as coefficients can be factored into products of linear and/or irreducible quadratic factors.
Every complex polynomial function of degree n has exactly n zeros and can be factored into a product of n linear factors. If its coefficient are real then those zeros that are complex numbers always occur as conjugate pairs. As a result, if is a complex zero, so is . Consequently, when the linear factors and and of function are multiplied we have
This second degree polynomial has real coefficient and is irreducible (over real numbers). Thus it is true that the factors of function are either linear or irreducible quadratic factors.
University Calculus: Early Transcendentals (4th Edition)
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