Find the value of $k,$ if $x-1$ is a factor of $4 x^{3}+3 x^{2}-4 x+k$.
$4$
$-3$
$3$
$-4$
Verify : $x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$
Write the following cubes in the expanded form : $(5 p-3 q)^{3}$
Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $x^{10}+y^{3}+t^{50}$
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.
Verify that $x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]$