Which of the following expressions is NOT a polynomial in $x$?

• A. $9-x$
• B. $4x^{\frac{1}{2}}+6$
• C. $x^3+2x-7$
• D. $3x^2-5x+1$

Answer: (B)

Verified step by step guidance

1. Recall that a polynomial in \( x \) is an expression consisting of terms with non-negative integer exponents of \( x \), combined using addition, subtraction, and multiplication by constants.
2. Examine each expression to identify the exponents of \( x \):
3. 1. \( 9 - x \) has \( x \) to the power of 1, which is a non-negative integer, so it is a polynomial.
4. 2. \( 4x^{\frac{1}{2}} + 6 \) has \( x \) raised to the power of \( \frac{1}{2} \), which is not an integer, so this is NOT a polynomial.
5. 3. \( x^{3} + 2x - 7 \) and \( 3x^{2} - 5x + 1 \) both have integer exponents (3, 1, 2, 1, 0), so they are polynomials.