Reduce the Expression: Simplifying (16x^4-4x^3)/(2x)

Let's simplify the given expression:

$\frac{16x^4-4x^3}{2x}$Remember that we can reduce complete expressions only when both the numerator and denominator are completely factored into multiplication expressions,

For this, we'll use factorization. We must first determine whether in the numerator we can factor out a common term. Following this we will proceed to reduce the possible expressions in the resulting fraction:

$\frac{16x^4-4x^3}{2x} \\ \frac{4x^3(4x-1)}{2x} \\ \frac{2x^2(4x-1)}{1}\\ \downarrow\\ \boxed{ 2x^2(4x-1)}$Let's expand the parentheses in the resulting expression and we can therefore determine that the correct answer is answer a.