Final answer:
Expression b, 6x³+x², is a polynomial because it is comprised of terms with variables raised to positive integer exponents.
It fits the definition of a polynomial, which includes expressions in the form ax^n+bx^m+...+k, where n and m are non-negative integers, and a, b, and k are constants.
Step-by-step explanation:
To determine which algebraic expression is a polynomial, we need to look for expressions that are sums of terms of variables raised to non-negative integer exponents. Here are the given expressions for evaluation:
- a. 4x²+3x
- b. 6x³+x²
- c. 8x²
- d. 2x⁴
Expression a. 4x²+3x is not a polynomial because it contains '3x' which is not properly formatted as a term. Expression b. 6x³+x² is a polynomial because it consists of terms with variables raised to positive integer exponents and no variables are in the denominator. Expression c. 8x² is also a polynomial for the same reasons. Expression d. 2x⁴ is a polynomial as well. The correct answer here is b. 6x³+x², which is a polynomial, and it fulfills the definition of a polynomial.
A polynomial is generally of the form axⁿ+bxᵐ+...+k, where n and m are non-negative integers, and a, b, and k are constants. Expression b adheres to this form.