21.2 - Finding Irreducible Factors
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Practice Questions
Test your understanding with targeted questions
Identify the root of f(x) = x - 3.
💡 Hint: What value makes f(x) equal to 0?
What defines a monic polynomial?
💡 Hint: Consider the highest degree term.
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Interactive Quizzes
Quick quizzes to reinforce your learning
A polynomial of degree n can have at most how many roots?
💡 Hint: Consider how roots relate to the degree.
True or False: Every polynomial has at least one real root.
💡 Hint: Think about polynomials with even degrees and positive leading coefficients.
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Challenge Problems
Push your limits with advanced challenges
Factor the polynomial f(x) = x^4 - 5x^2 + 6.
💡 Hint: Try substituting a new variable to simplify the expression.
Prove that the polynomial x^5 + x + 1 has no rational roots.
💡 Hint: Evaluate potential candidates and see if f(α) = 0 is ever true for them.
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