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
$x+6$
$12$
$8$
$0$
$3$
Factorise :
$2 x^{3}-3 x^{2}-17 x+30$
Verify whether $2$ and $5$ are zeros of the polynomial $x^{2}-2 x-15$ or not.
Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$
Evaluate
$(555)^{2}$
Factorise the following quadratic polynomials by splitting the middle term
$x^{2}-12 x+20$
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