We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript 1/N], namely Q(w[superscript 1; subscript N]x[superscript 1/N]) x Q(w[superscript 2; subscript N ]x[superscript 1/N]) ... Q(w[superscript N ; subscript N]x[superscript 1/N]), where "w[subscript n]" is the "N"th root of 1.