Evaluate the following using suitable identities

$(105)^{3}$

In the polynomial $5 x^{3}-3 x^{2}+11 x-4,$ the coefficient of $x^{2}$ is......

Write the coefficient of $x^{2}$ in the following polynomials

$5-7 x-3 x^{2}$

If $x^{2}-10 x+21=(x+m)(x+n)$ then $m+n=\ldots \ldots \ldots$

Factorise

$8 x^{3}-26 x^{2}+13 x+5$

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

$x-4$