Final answer:
The coefficient of x in the expanded form of (x⁴ + x³ + x² + x + 1)⁴ is 4, found by understanding that the term x can be obtained by choosing x from one factor and the constant term from the other three factors in four different ways.
Step-by-step explanation:
The question is asking for the coefficient of x when the expression (x4 + x3 + x2 + x + 1)4 is expanded. To find this coefficient, we need to consider the ways in which the term x can be formed when the expression is expanded using the binomial theorem. The term x can only be obtained when we pick the x term from one of the four factors and the constant term from the remaining three factors. This can happen in 4 different ways because there are four factors to choose from for where to pick the x term. Therefore, we need to multiply the coefficient of the x term in the original expression, which is 1, by 4, since there are four ways to obtain x after expansion. Hence, the coefficient of x is 4.