Final answer:
Expressions B, C, and D are classified as polynomials because they consist of variables with non-negative integer exponents and constant coefficients. Expression A is not a polynomial due to the presence of a fractional exponent.
Step-by-step explanation:
To determine which expressions are polynomials, we need to check if they meet the definition of a polynomial, which typically consists of a sum of products of variables and constants where the variables have non-negative integer exponents. Let's examine each of the provided expressions:
- A. 3y^2 (x^1/4) - This expression includes a fractional exponent (x^1/4), which is not allowed in polynomials.
- B. 8x^2 (3y) - This expression is a product of constants and variables with integer exponents, which is allowed in polynomials. So, this is a polynomial.
- C. 9x^2 (y/5) - Similar to B, this expression consists of a product of constants and variables with non-negative integer exponents, making it a polynomial.
- D. 4x^2 (y^5) - This expression also has variables with non-negative integer exponents and is therefore a polynomial.
Based on these analyses, expressions B, C, and D are polynomials, but A is not.