Math Problem Statement
Solution
Let's examine each function to determine whether it is a polynomial.
(a)
This is a product of polynomials, which is expanded as a polynomial. Polynomials are defined as expressions with non-negative integer powers of , and this meets that requirement. Answer: Yes, this is a polynomial.
(b)
This function contains the term , which has a negative power of (i.e., ). A polynomial function cannot have negative exponents. Answer: No, this is not a polynomial.
(c)
This function is a sum of terms with positive integer exponents of . It fits the definition of a polynomial. Answer: Yes, this is a polynomial.
(d)
This function contains a square root of , which is equivalent to . Since polynomial exponents must be non-negative integers, this is not a polynomial. Answer: No, this is not a polynomial.
Would you like further details on any of these functions or have additional questions?
Related Questions:
- What are the specific conditions for a function to be classified as a polynomial?
- How do negative exponents affect the classification of a polynomial?
- What is the process for expanding into standard polynomial form?
- Why does the presence of square roots or fractional powers exclude a function from being a polynomial?
- What are common misconceptions when identifying polynomials?
Tip:
Remember, a polynomial function's terms must all have non-negative integer exponents.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Exponents
Square Roots
Formulas
Polynomial function: P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_0
Exponent rule: x^(m/n) = n√(x^m)
Theorems
Polynomials cannot have negative or fractional exponents
A product of polynomials is a polynomial
Suitable Grade Level
Grades 9-12
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