Practice Number Of Roots For Degree N Polynomial (21.2)

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8 questions

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6 sample questions

Question 1.
What is a root of a polynomial?
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Remember the definition of a root.
Question 2.
What is the degree of the polynomial f(x) = 3x⁵ + 2x⁴ - x + 7?
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Look for the term with the highest power.
3Question 3.
How many roots can a polynomial of degree n have?
- n-1
- n
- n+1
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Consider the definition of degree.
4Question 4.
Is the statement 'A quadratic polynomial can have at most two linear factors' true or false?
- True
- False
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Think about the degree again.
Question 5.
Consider the polynomial f(x) = x⁵ - 5x³ + 4x. Factor it completely over the reals and identify its roots.
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Look for common factors first.
Question 6.
Demonstrate that the polynomial f(x) = 2x⁴ + x³ - 4x² - 2x + 1 is irreducible over the rationals.
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Try picking potential rational roots to start.

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