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

The $G.C.D.$ and $L.C.M.$ of two polynomials $p(x)$ and $q(x)$ are $x(x+a)$ and $12x^2(x+a)(x^2-a^2)$ respectively. If $p(x) = 4x(x+a)^2$,find $q(x)$.

The $L.C.M.$ of $(x^{2}-y^{2})$,$(x^{3}-y^{3})$,and $(x^{3}-x^{2}y-xy^{2}+y^{3})$ is

The $H.C.F.$ (Highest Common Factor) of two polynomials is $(y-7)$ and their $L.C.M.$ is $y^{3}-10y^{2}+11y+70$. If one of the polynomials is $y^{2}-5y-14$,find the other.

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

Find the $L.C.M.$ of the polynomials $30 x^{2}+13 x-3$ and $25 x^{2}-30 x+9$.