The value of $249^{2}-248^{2}$ is

What should be subtracted from $p(x)=x^{2}+9 x+20,$ so that the resulting polynomial is divisible by $x+2 ?$

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

Expand

$\left(x-\frac{1}{2}\right)^{2}$

Without actually calculating the cubes, find the value of :

$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$