Final answer:
The algebraic expression that is a polynomial is A. 4x²−3x+x², as it consists of variables raised to non-negative integer powers without any root operations or negative exponents.
Step-by-step explanation:
The algebraic expression that is a polynomial is A. 4x²−3x+x². A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
Let's examine each option:
- Option A: 4x²−3x+x². This is the sum of terms with variables raised to non-negative integer powers, so it is a polynomial.
- Option B: −6x³+x²−√5. This would be a polynomial were it not for the √5. A polynomial cannot contain roots.
- Option C: 8x²+√x. This contains a square root of a variable, which is not allowed in a polynomial.
- Option D: −2x⁴+√3/2·x. The √3/2 is not a term with a variable, but the x beside it suggests the term is part of the polynomial, which makes it not a true polynomial as it has a square root factor.
Therefore, option A is the only true polynomial. Polynomials are often used to represent real-world scenarios and are an essential part of algebra and calculus.