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