21..1 - Methods for Finding Irreducible Factors
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Practice Questions
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What is a root of a polynomial?
💡 Hint: Think about what happens when you substitute a number into the polynomial.
Define a monic polynomial.
💡 Hint: What is special about the leading coefficient?
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Interactive Quizzes
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What does the factor theorem state?
💡 Hint: Think about what happens if substituting α into the polynomial results in zero.
True or False: A polynomial of degree n can have at most n roots.
💡 Hint: Relate to polynomial properties.
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Challenge Problems
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Given the polynomial x^5 + x^3 + x^2, find its irreducible factors over the field of integers.
💡 Hint: Look for integers that satisfy the equation.
Using the polynomial x^4 + 2x^2 + 1, identify and justify its potential irreducibility.
💡 Hint: Check if your polynomial resembles the form of squares.
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