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

Write the degree of the following polynomial: $8x^{5} + 3x^{2} - 4x + 7$.

State whether the following statement is true or false:
$x^{2}-8x+12 = (x-6)(x-2)$

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}+10x+16$

Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x + x^{2} - 1$
$(ii)$ $3x - 5$

Write whether the following statement is True or False. Justify your answer.
$\frac{1}{\sqrt{5}} x^{\frac{1}{2}} + 1$ is a polynomial.