What is the HCF ofacx³ + bcx² + adx² + acdx + bdx + bcd and adx³ + acx² + bdx² + bcx + acdx + bcd if HCF (c, d) = 1, c ≠ d?

acx³ + bcx² + adx² + acdx + bdx + bcd    —-(i)

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

 For equation (i),

     acx³ +adx²+acdx + bcx² + bdx + bcd

     

$$ax(cx^2+dx+cd) + b(cx^2+dx+cd)$$

   

$$(ax+b)(cx^2+dx+cd)$$
 For equation (ii),

   adx³ + acx² + bdx² + bcx + acdx + bcd

   adx³ + acx² +acdx + bdx² + bcx + bcd

     

$$ax(dx^2+cx+cd) + b(dx^2+cx+cd)$$

  

$$(ax+b)(dx^2+cx+cd)$$

So, HCF is ( ax + b ). 

Answer (D) – ax+b