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

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

$x-4$

Factorise

$49 x^{2}-35 x+6$

Find the value of $a$, if $x-a$ is a factor of $x^{3}-a x^{2}+2 x+a-1$.

Evaluate

$77 \times 83$