Math Problem Statement
Solution
To solve this problem, we need to apply the Rational Zeros Theorem to the polynomial function:
Step-by-Step Explanation
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Identify the coefficients:
- The leading coefficient is (coefficient of ).
- The constant term is .
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Rational Zeros Theorem:
- The potential rational zeros are in the form , where:
- is a factor of the constant term (28).
- is a factor of the leading coefficient (2).
- The potential rational zeros are in the form , where:
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Factors of the constant term (28):
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Factors of the leading coefficient (2):
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Form all combinations : Simplifying the fractions:
Answer Verification
From the options provided:
- Option D matches the correct potential rational zeros list, including .
Correct Answer: D
Would you like a detailed explanation on any part of the solution?
Related Questions:
- How do you find factors of a number for the Rational Zeros Theorem?
- What happens if the polynomial has a leading coefficient of 1?
- Can the Rational Zeros Theorem identify all real zeros of a polynomial?
- What is the next step if you want to verify whether a potential zero is an actual zero?
- How do you perform synthetic division to test potential zeros?
Tip:
Always check the simplification of fractions when listing potential rational zeros to avoid redundancy.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Rational Zeros Theorem
Formulas
Rational Zeros Theorem: p/q, where p is a factor of the constant term and q is a factor of the leading coefficient
Theorems
Rational Zeros Theorem
Suitable Grade Level
Grade 11-12
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