Factorise : $49 a^{2}+70 a b+25 b^{2}$
Divide the polynomial $3 x^{4}-4 x^{3}-3 x-1$ by $x-1$.
Write the following cubes in expanded form : $\left[\frac{3}{2} x+1\right]^{3}$
Find the zero of the polynomial : $p(x) = x -5$
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.