Practice The Gcd Of Polynomials Over Fields (20.3) - Polynomials Over Fields and Properties

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9 questions

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Exercise
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6 sample questions

Question 1.
Define the GCD of two polynomials.
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Think about the concept of GCD from integers.
Question 2.
Give an example of an irreducible polynomial.
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Consider polynomials you cannot factor over a given field.
3Question 3.
What is the GCD of two polynomials?
- The smallest polynomial
- The largest polynomial that divides both
- Any polynomial that divides both
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Think about what 'greatest' means.
4Question 4.
A polynomial is irreducible if:
- True
- False
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Consider the definition of irreducibility.
Question 5.
Find the GCD of x^4 - 1 and x^2 - 1 using polynomial division.
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Start the division process carefully.
Question 6.
Show that the polynomial 3x^3 + 6x^2 + 3x is reducible. Factor it completely.
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Look for common factors first!

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