Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x-1$.

For the polynomial $p(x),$ if $p(7)=0,$ then .......... is a factor of $p(x)$.

Using the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x - 6$.

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}+14x+33$

Factorise the following quadratic polynomial by splitting the middle term:
$x^{2}-12x+20$

From the following polynomials,find out which of them has $(x-1)$ as a factor:
$p(x) = 2x^3 + 5x^2 - x - 6$