Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x -1$.
$2$
$3$
$4$
$5$
Use suitable identities to find the products : $(x+4)(x+10)$
Verify : $x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$
Expand each of the following, using suitable identities : $(x+2 y+4 z)^{2}$
Factorise : $x^{3}-3 x^{2}-9 x-5$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+3 x^{3}+3 x^{2}+x+1$.