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

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

Write the degree of the following polynomial: $5$.

If $p(3) = 0$ for a polynomial $p(x)$,state one factor of $p(x)$.

Give an example of a polynomial,which is:
$(i)$ monomial of degree $1$
$(ii)$ binomial of degree $20$
$(iii)$ trinomial of degree $2$

If $x+3$ is a factor of $x^{3}+12x^{2}+ax+60$,then $a = \ldots$