Math Problem Statement
Solution
To list all possible rational zeros using the Rational Zeros Theorem for the polynomial , we follow these steps:
Rational Zeros Theorem:
The possible rational zeros of a polynomial are of the form: where:
- is a factor of the constant term (here, ),
- is a factor of the leading coefficient (here, since the coefficient of is 1).
Step 1: Identify the factors of the constant term (8).
The factors of 8 are:
Step 2: Identify the factors of the leading coefficient (1).
The factors of 1 are:
Step 3: Form the possible rational zeros.
The possible rational zeros are:
Thus, the set of possible rational zeros is:
Conclusion:
The correct option from the choices is (b).
Would you like more details or have any questions?
Here are 5 related questions you might want to explore:
- How do you determine if a given rational zero is an actual root of the polynomial?
- What are the steps for synthetic division when testing for rational roots?
- How does the Rational Zeros Theorem relate to the Fundamental Theorem of Algebra?
- Can the Rational Zeros Theorem be applied to polynomials with non-integer coefficients?
- What other methods can be used to find the roots of a polynomial apart from the Rational Zeros Theorem?
Tip: After listing all possible rational zeros, use synthetic or long division to check which ones are actual zeros of the polynomial!
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Rational Zeros Theorem
Formulas
-
Theorems
Rational Zeros Theorem
Suitable Grade Level
Grades 9-12
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