Math Problem Statement

Which expression is NOT a polynomial?

Solution

The question asks: Which expression is NOT a polynomial?

To analyze the options:

  1. 13x3\frac{1}{3}x^3: This is a polynomial because it has a term x3x^3 with a fractional coefficient, and all powers of xx are non-negative integers.

  2. 12x12x: This is a polynomial because it consists of one term, 12x12x, where the power of xx is 1 (a non-negative integer).

  3. x3+1x\frac{x^3 + 1}{x}: This is NOT a polynomial because it involves division by xx, resulting in a term 1x\frac{1}{x}, which is x1x^{-1}, and the power 1-1 is a negative integer. Polynomials cannot have negative powers.

  4. x22xx^2 - 2x: This is a polynomial because it consists of terms x2x^2 and 2x-2x, where both powers of xx are non-negative integers.

Correct Answer:

The expression x3+1x\frac{x^3 + 1}{x} is NOT a polynomial.


Would you like a detailed explanation of polynomials or have any additional questions?

Related Questions:

  1. What are the key characteristics of a polynomial?
  2. Can fractional coefficients exist in polynomials?
  3. Why are negative powers not allowed in polynomials?
  4. How are rational expressions different from polynomials?
  5. 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