Question

Select all of the following expressions that are polynomials. (2 points)
A. 1/2 x^3 + 2x^2 - 5
B. 3x 1/2 + 10
C. 4x^-2 + 9x + 6
D. -4x + 1

Answer 1

A polynomial is an expression made up of variables raised to non-negative integer powers, along with constant coefficients. Let's analyze each given expression:

A. \( \frac{1}{2} x^3 + 2x^2 - 5 \) - This is a polynomial because it comprises terms where the variables are raised to non-negative integer powers.

B. \( 3x^{1/2} + 10 \) - This is **not** a polynomial because the exponent \( \frac{1}{2} \) is a fraction (specifically, a square root), which does not meet the criteria for polynomial terms.

C. \( 4x^{-2} + 9x + 6 \) - This is **not** a polynomial because the term \( 4x^{-2} \) has a negative exponent, which does not meet the criteria for polynomial terms.

D. \( -4x + 1 \) - This is a polynomial because it consists of terms with variables raised to non-negative integer powers.

Thus, the polynomials from the options provided are:

- A. \( \frac{1}{2} x^3 + 2x^2 - 5 \)
- D. \( -4x + 1 \)

The final answer is: **A and D**.