With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x+4$

If $x+1$ is a factor of $a x^{3}+x^{2}-2 x+4 a-9,$ find the value of $a$.

Check whether $p(x)$ is a multiple of $g(x)$ or not :

$p(x)=2 x^{3}-11 x^{2}-4 x+5, \quad g(x)=2 x+1$

Evaluate

$(1002)^{2}$

Verify whether the following are True or False:

$-3$ is a zero of $x-3$

Verify whether the following are True or False:

$-3$ is a zero of $y^{2}+y-6.$