From the following polynomials find out which of them has $(x-1)$ as a factor
$x^{3}+4 x^{2}+x-6$
$(x-1)$ is a factor.
If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$
Without finding the cubes, factorise $(x-y)^{3}+(y-z)^{3}+(z-x)^{3} .$
Check whether the polynomial
$p(x)=x^{3}+9 x^{2}+26 x+24$ is a multiple of $x+2$ or not.
Give possible expressions for the length and breadth of the rectangle whose area is given by $4 a^{2}+4 a-3$
Factorise
$27 x^{3}-y^{3}+64 z^{3}+36 x y z$
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