Practice Factorization Of Polynomials (20.4) - Polynomials Over Fields and Properties

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8 questions

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6 sample questions

Question 1.
Define a polynomial.
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Think about its general form.
Question 2.
What does it mean for a polynomial to be irreducible?
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Consider what factoring entails.
3Question 3.
What defines an irreducible polynomial?
- It cannot be factored at all.
- It can be factored but not into linear factors.
- It cannot be factored into non-constant polynomials.
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Consider what 'factoring' means.
4Question 4.
Is the GCD of two polynomials always unique?
- True
- False
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Think about how polynomials can be expressed differently.
Question 5.
Determine if the polynomial 3x^3 + 6x^2 + 3x is reducible or irreducible.
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Check for common factors.
Question 6.
Calculate the GCD of 4x^4 + 8x^2 and 2x^2.
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Use polynomial division to find common factors.

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