What is the HCF of acx3 + bcx2 +  adx2 + acdx + bdx + bcd and adx3 + acx2 + bdx2 + bcx + acdx + bcd if HCF (c, d) = 1, c ≠ d?

Calculation:

Expression 1:

acx3 + bcx2 +  adx2 + acdx + bdx + bcd

(acx3 + bcx2) + (adx2 + bdx) + (acdx + bcd)

cx²(ax + b) + dx (ax + b) + cd(ax + b)

(ax + b)(cx² + dx + cd)

Expression 2:

dx3 + acx2 + bdx2 + bcx + acdx + bcd

(adx3 + bdx2) + (acx2 + bcx) + (acdx + bcd)

dx²(ax + b) + cx(ax + b) + cd(ax + b) 

(ax + b)(dx² + cx + cd)

We know that, HCF is the highest power of each common prime factor.

∴ HCF = ax + b