If $(x-1)$ is the $H.C.F.$ of $(x^{2}-1)$ and $[p x^{2}-q(x+1)]$,then:

The $L.C.M.$ and $H.C.F.$ of two polynomials $p(x)$ and $q(x)$ are $36 x^{3}(x+a)(x^{3}-a^{3})$ and $x^{2}(x-a)$ respectively. If $p(x)=4 x^{2}(x^{2}-a^{2})$,find $q(x)$.

The $H.C.F.$ of two expressions $p$ and $q$ is $1$. Their $L.C.M.$ is

For what value of $a,$ the $G.C.D.$ of $x^{2}-2x-24$ and $x^{2}-ax-6$ is $(x-6)$?

Find the $G.C.D.$ of $8(x^{4}-16)$ and $12(x^{3}-8)$.

The product of two non-zero expressions is $(x+y+z) p^{3}$. If their $H.C.F.$ is $p^{2}$,their $L.C.M.$ is