Write the degree of each of the following polynomials
$x^{8}-6561$
$10$
$14$
$8$
$12$
Verify whether the following are True or False:
$-\frac{1}{3}$ is a zero of $3 x+1$
On dividing $p(x)=x^{3}+2 x^{2}-5 a x-7$ by $(x+1),$ the remainder is $R _{1}$ and on dividing $q(x)=x^{3}+a x^{2}-12 x+6$ by $(x-2), \quad$ the remainder is $R _{2} .$ If $2 R _{1}+ R _{2}=6,$ then find the value of $a$.
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $\frac{\pi}{6} x+x^{2}-1$
$(ii)$ $3 x-5$
From the following polynomials find out which of them has $(x+1)$ as a factor
$x^{3}+10 x^{2}+23 x+14$
The factorisation of $4 x^{2}+8 x+3$ is