Find the value of $k$ if $f(x) = x^{3} - kx^{2} + 11x - 6$ and $(x - 1)$ is a factor of $f(x)$.

Let $f(x) = a_{0}x^{n} + a_{1}x^{n-1} + a_{2}x^{n-2} + \ldots + a_{n-1}x + a_{n}$,where $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ are constants. If $f(x)$ is divided by $ax - b$,then the remainder is:

Resolve into factors: $9(3 x+5 y)^{2}-12(3 x+5 y)(2 x+3 y)+4(2 x+3 y)^{2}$

Resolve into factors: $81 x^{2} y^{2}+108 x y z+36 z^{2}$.

If $a-b=1$ and $ab=6$,then what is the value of $(a^3-b^3)$?

If $(x^{3/2} - x y^{1/2} + x^{1/2} y - y^{3/2})$ is divided by $(x^{1/2} - y^{1/2})$,then the quotient is