Final answer:
The expression 4x^3 - 3x + 1/x should be represented as p(x)/k, where p(x) = 4x^3 - 3x and k = 1.
Step-by-step explanation:
The expression 4x^3 - 3x + 1/x should be represented in the form of a fraction where the numerator is a polynomial and the denominator is an integer. When we have a term with a negative exponent, such as 1/x or x^-1, it signifies division. Hence, to write the given expression in the desired form, we simply identify the polynomial part as p(x), which is 4x^3 - 3x, and the integer k in the denominator as 1 because the term 1/x can be expressed as x^-1. Therefore, the correct representation of the expression would be p(x)/k, where p(x) = 4x^3 - 3x and k = 1. So the correct representation is option b) p(x).