Practice Example Of A Polynomial Factorization (21..2)

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9 questions

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6 sample questions

Question 1.
Define what a root of a polynomial is.
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Think of simple polynomials and what values make them zero.
Question 2.
What does it mean for a polynomial to be monic?
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Look at the term with the highest degree.
3Question 3.
What is a root of a polynomial?
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Consider simple examples of roots.
4Question 4.
True or False: A degree n polynomial can have more than n roots.
- True
- False
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Think of the definition of polynomial degree.
Question 5.
Prove algebraically that a polynomial of degree 5 can have at most 5 roots.
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Use polynomial long division.
Question 6.
Given the polynomial x⁵ + x + 1, determine its irreducibility over the integers.
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Test possible rational roots derived from factors of the constant term.

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