20.6 - Factor Theorem for Polynomials Over Fields
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Practice Questions
Test your understanding with targeted questions
Evaluate f(3) for f(x) = x^2 - 9 before identifying a factor.
💡 Hint: Plug in x = 3 into the polynomial.
Check if (x - 1) is a factor of f(x) = x^2 - x.
💡 Hint: Evaluate f(x) at x = 1.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Factor Theorem state about a polynomial and its value at a root?
💡 Hint: Remember what happens at roots.
If f(0) = 5, does (x - 0) divide the polynomial f?
💡 Hint: Consider how factors relate to roots.
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Challenge Problems
Push your limits with advanced challenges
Prove that if a polynomial of degree n has n distinct roots, then it can be expressed as a product of linear factors.
💡 Hint: Break down the proof by induction over the degree.
Given a polynomial p(x) = x^4 - 16, find its factors and confirm the roots using the Factor Theorem.
💡 Hint: Consider how to approach factorization in steps.
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