Explanation

Note that a⁴+2a³+3a²+2a+1 expands exactly as (a²+a+1)²: squaring gives a⁴+a²+1+2a³+2a²+2a, which matches term by term. Similarly a⁶−2a³+1 = (a³−1)² = ((a−1)(a²+a+1))² = (a−1)²(a²+a+1)². The greatest common divisor of the two polynomials is therefore (a²+a+1)² — option C.