Find $p(1), p(2)$ and $p(4)$ for each of the following polynomials
$p(x)=x^{3}+9 x^{2}+23 x+15$
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 $12 x^{3}-31 x^{2}-18 x+9$
If $x^{2}-10 x+21=(x+m)(x+n)$ then $m+n=\ldots \ldots \ldots$
On dividing $16 x^{2}-24 x+9$ by $4 x-3,$ find the remainder.
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x+x^{2}-1$
$(ii)$ $3 x-5$