Which of the following is NOT a polynomial?

Which of the following is NOT a polynomial?

• A. sqrt(x)
• B. 2x^2 + 3x
• C. 7
• D. 4x

Answer: (A)

Polynomials are expressions formed by adding or subtracting constant multiples of powers of the variable where the powers are nonnegative integers, and there are only finitely many terms. That means every term looks like a constant times x^n with n a whole-number exponent. The square root of x uses a fractional exponent, x^(1/2), which is not a nonnegative integer power, so it cannot be written as a finite sum of terms with such exponents. In contrast, 2x^2 + 3x has terms with exponents 2 and 1, and 4x is x to the first power, while 7 is x^0. These fit the polynomial form and are defined for all real x. Therefore, the square root of x is not a polynomial.

Polynomials are expressions formed by adding or subtracting constant multiples of powers of the variable where the powers are nonnegative integers, and there are only finitely many terms. That means every term looks like a constant times x^n with n a whole-number exponent.

The square root of x uses a fractional exponent, x^(1/2), which is not a nonnegative integer power, so it cannot be written as a finite sum of terms with such exponents. In contrast, 2x^2 + 3x has terms with exponents 2 and 1, and 4x is x to the first power, while 7 is x^0. These fit the polynomial form and are defined for all real x. Therefore, the square root of x is not a polynomial.