Factorise the following quadratic polynomials by splitting the middle term

$x^{2}-4 x-77$

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

$x-6$

From the following polynomials find out which of them has $(x+1)$ as a factor

$x^{3}+10 x^{2}+23 x+14$

Using suitable identity, evaluate the following:

$103^{3}$

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

$x+4$

Show that :

$2 x-3$ is a factor of $x+2 x^{3}-9 x^{2}+12$