21.2.2 - Conditions for Quadratic Factors
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Practice Questions
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What is the definition of a root of a polynomial?
💡 Hint: Think about the values that make the polynomial equal zero.
How many roots can a polynomial of degree 3 have?
💡 Hint: The number of roots corresponds to the degree of the polynomial.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the maximum number of roots a polynomial of degree 5 can have?
💡 Hint: Remember the definition of polynomial degree.
True or False: All monic polynomials can be factored into irreducible factors.
💡 Hint: Think about the properties of monic polynomials and factorization.
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Challenge Problems
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Show that the polynomial 2x^3 + 4x^2 + 2x can be factored into irreducible factors.
💡 Hint: Look for common factors first.
Prove that a polynomial of degree n will have at least one root in a field.
💡 Hint: Consider how polynomials behave on an interval.
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