Evaluate the following using suitable identities: $(105)^{3}$

Find the value of the polynomial $x^{2}-7x+12$ at $x=1$.

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 4$.

Find $p(0)$,$p(1)$,and $p(-2)$ for the following polynomial:
$p(x) = 10x - 4x^{2} - 3$

Check whether $(x-1)$ is a factor of the polynomial $p(x) = x^{3}-7x^{2}+14x-8$.

Dividing $p(x) = x^{2} + 12x + 36$ by $(x + 5)$,the remainder is.......