Math Problem Statement
Solution
The question asks: Which expression is NOT a polynomial?
To analyze the options:
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: This is a polynomial because it has a term with a fractional coefficient, and all powers of are non-negative integers.
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: This is a polynomial because it consists of one term, , where the power of is 1 (a non-negative integer).
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: This is NOT a polynomial because it involves division by , resulting in a term , which is , and the power is a negative integer. Polynomials cannot have negative powers.
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: This is a polynomial because it consists of terms and , where both powers of are non-negative integers.
Correct Answer:
The expression is NOT a polynomial.
Would you like a detailed explanation of polynomials or have any additional questions?
Related Questions:
- What are the key characteristics of a polynomial?
- Can fractional coefficients exist in polynomials?
- Why are negative powers not allowed in polynomials?
- How are rational expressions different from polynomials?
- Can a polynomial have fractional exponents?
Tip:
Polynomials are defined as expressions with variables raised to non-negative integer powers and have coefficients that can be real or complex numbers.
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Math Problem Analysis
Mathematical Concepts
Polynomials
Exponents
Rational Expressions
Formulas
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Theorems
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Suitable Grade Level
Grades 8-10