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. (a) are x and x 1 the only monic fsp polynomials of degree 1? (b) note that x2, x2 1, x2 x, and x2 + x + 1 have fsp. list all the monic fsp polynomials of degree 2. (c) observe that x2 and x2 x arise from degree 1 cases, but x2 1 and x2 + x + 1 are new, not expressible as a product of two smaller fsp polynomials. list all the new monic fsp polynomials of degree 3. can you nd all the new monic fsp polynomials of degree 4 ? (d) many examples found above have integer coecients. do answers change if we allow coecients to be any real numbers? or if we allow polynomials whose coecients are complex numbers?