What is the HCF of the polynomials x⁸ + x⁴ + 1 and x⁴ + x² + 1?

x⁴ + x² + 1 = (x² + x + 1)(x² − x + 1). Also x⁸ + x⁴ + 1 = (x⁴ + x² + 1)(x⁴ − x² + 1). So x⁴ + x² + 1 divides x⁸ + x⁴ + 1 completely. Hence HCF = x⁴ + x² + 1.