Question

The product of two expressions is $a^4-9a^2+4a+12$ and their H.C.F. is $a-2$. Find their L.C.M.

Answer 1

Given : Product of two expressions $=a^4-9a^2+4a+12$ and their H.C.F $=(a-2)$

Using the result, Product of two expressions $=$ product of their H.C.F. and L.C.M.

$⟹$ $a^4-9a^2+4a+12=H.C.F.\times L.C.M.$

$⟹$ $a^4-9a^2+4a+12=(a-2)\times LCM$

By using synthetic division for first equation we get,

$(a-2)(a-2)(a+1)(a+3)=(a-2)\times LCM$

$\therefore$ $LCM=\frac{(a-2)(a-2)(a+1)(a+3)}{(a-2)}$

$⟹$ $LCM=(a-2)(a+1)(a+3)$.