A polynomial f(x) has the factor-square property (or FSP) if f(x) is a factor of f(x²). For instance, g(x) = x – 1 and h(x) = x have FSP, but k(x) = x + 2 does not. Reason: x-1 is a factor of x² – 1, and x is a factor of x², but +2 is not a factor of x² +2. Multiplying by a nonzero constant "preserves" FSP, so we restrict attention to poly- nomials that are monic (i.e., have 1 as highest-degree coefficient). What patterns do monic FSP polynomials satisfy? To make progress on this topic, investigate the following questions and justify your answers.
Are x and x – 1 the only monic FSP polynomials of degree 1?