For the polynomial $p(x),$ if $p(7)=0,$ then ………. is a factor of $p(x)$.

Write the coefficient of $x^{2}$ in each of the following:

$(i)$ $\frac{\pi}{6} x+x^{2}-1$

$(ii)$ $3 x-5$

Classify the following as a constant, linear,quadratic and cubic polynomials:

$5 t-\sqrt{7}$

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

If the polynomial $a x^{3}+4 x^{2}+3 x-4$ and polynomial $x^{3}-4 x+a$ leave the same remainder when each is divided by $x-3,$ find the value of $a$.