If $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$

Factorise $16 x^{2}-40 x y+25 y^{2}$.

For the polynomial $\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6},$ write:
$(i)$ the degree of the polynomial
$(ii)$ the coefficient of $x^{3}$
$(iii)$ the coefficient of $x^{6}$
$(iv)$ the constant term

Find the zero of the polynomial $p(x)=5 x-8$.

Verify whether the following is True or False:
$-\frac{1}{3}$ is a zero of $3x + 1$.

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 4$.