Explanation

Factor the first polynomial by grouping: (acx³ + adx² + acdx) + (bcx² + bdx + bcd) = ax(cx² + dx + cd) + b(cx² + dx + cd) = (ax + b)(cx² + dx + cd). Likewise the second is (adx³ + acx² + acdx) + (bdx² + bcx + bcd) = (ax + b)(dx² + cx + cd). Both share the factor (ax + b). The remaining quadratics share no further factor forced by the given conditions (their difference is (c−d)x(x−1), and with c ≠ d and HCF(c, d) = 1 neither x nor x−1 divides both), so the HCF is exactly ax + b. The answer is (D).