By using the factor theorem, show that $(x-3)$ is a factor of the polynomial $12 x^{3}-31 x^{2}-18 x+9$ and then factorise $12 x^{3}-31 x^{2}-18 x+9$

Write the degree of the following polynomials

$7 x^{3}-9 x^{2}+4 x-22$

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 in each of the following cases

$p(t)=7 t-21$

Factorise

$9 x^{2}+42 x+49$