Final answer:
The algebraic expression that is a polynomial is D) (7mn + 3m/2+5n/4), since it's the only option that strictly follows the definition of a polynomial, consisting of variables to non-negative integer powers and coefficients, without variables in the denominator or roots.
Step-by-step explanation:
The question asks which algebraic expression is a polynomial. A polynomial is an algebraic expression that consists of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Expressions with variables in the denominator, variable exponents, or involving roots (other than squares, cubes, etc. as they can be written with exponents) are not polynomials.
- A) (3m²n-2m/n+1/n) - This expression cannot be a polynomial because of the variables in the denominators of the terms -2m/n and +1/n.
- B) (2mn/5-√m/4+4m⁵) - This expression cannot be a polynomial because it includes a square root, √m, which cannot be expressed as a variable to a non-negative integer power.
- C) (4m³-n²-3mn⁵+√8) - This expression cannot be a polynomial because of the square root, √8, even though the rest of the terms do fit the criteria for a polynomial.
- D) (7mn + 3m/2+5n/4) - This expression is a polynomial. It is a sum of terms where each term is a product of variables to non-negative integer powers and coefficients, which includes the rational coefficients 3/2 and 5/4.
Therefore, the correct answer is D) (7mn + 3m/2+5n/4), as it is the only option that fits the definition of a polynomial.