State why the following expression is not a polynomial. 4x^(-1)+6x Choose the correct answer below. A. The exponent of the variable is a rational number. B. The exponent of the variable is a negative integer. C. The expression is a quotient of polynomials, which cannot be simplified to a polynomial. D. The exponent of the variable is an irrational number.

Question

State why the following expression is not a polynomial.  4x^(-1)+6x Choose the correct answer below. A. The exponent of the variable is a rational number. B. The exponent of the variable is a negative integer. C. The expression is a quotient of polynomials, which cannot be simplified to a polynomial. D. The exponent of the variable is an irrational number.

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Identify Characteristics of Polynomial: Identify the characteristics of a polynomial. A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.Examine Given Expression: Examine the given expression 4x^(-1)+6x to see if it meets the criteria of a polynomial. We need to check if all the exponents of the variable x are non-negative integers.Identify Exponents of Variable: Identify the exponents of the variable x in the expression. The first term has an exponent of -1 (4x^(-1)) and the second term has an exponent of 1 (6x).Determine Exponents for Polynomial: Determine if the exponents of the variable x meet the criteria for a polynomial. The exponent -1 is a negative integer, which does not satisfy the condition of having non-negative integer exponents.Choose Correct Answer: Choose the correct answer based on the analysis. Since the expression contains a term with a negative exponent, it does not qualify as a polynomial. The correct answer is that the exponent of the variable is a negative integer.

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