Practice Conditions For Quadratic Factors (21.2.2)

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8 questions

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6 sample questions

Question 1.
What is the definition of a root of a polynomial?
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Think about the values that make the polynomial equal zero.
Question 2.
How many roots can a polynomial of degree 3 have?
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The number of roots corresponds to the degree of the polynomial.
3Question 3.
What is the maximum number of roots a polynomial of degree 5 can have?
- 5
- 4
- 6
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Remember the definition of polynomial degree.
4Question 4.
True or False: All monic polynomials can be factored into irreducible factors.
- True
- False
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Think about the properties of monic polynomials and factorization.
Question 5.
Show that the polynomial 2x^3 + 4x^2 + 2x can be factored into irreducible factors.
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Look for common factors first.
Question 6.
Prove that a polynomial of degree n will have at least one root in a field.
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Consider how polynomials behave on an interval.

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