Practice Possibilities Of Factors (21.2.1) - Roots of a Polynomial - Discrete Mathematics

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6 sample questions

Question 1.
What is a root of a polynomial?
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Look for where f(x) = 0.
Question 2.
What is the degree of the polynomial 3x^4 - 2x^2 + 7?
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Identify the highest power of x in the polynomial.
3Question 3.
What does a polynomial root signify?
- It means the polynomial has been factored.
- It is a value that makes the polynomial equal zero.
- It refers to the degree of the polynomial.
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Recall the relationship defined by the factor theorem.
4Question 4.
True or false: A polynomial of degree n can have more than n roots.
- True
- False
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Think about the relationship between degree and factors.
Question 5.
Given the polynomial f(x) = x^5 - 32, find its roots and confirm how many roots it has.
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Use the rational root theorem for finding potential roots.
Question 6.
Demonstrate how to factor the polynomial x^6 + 1 and identify its irreducible factors.
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Look for patterns or known factorizations.

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