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
$x+1$
$45$
$60$
$50$
$20$
Evaluate the following using suitable identities
$(105)^{3}$
Evaluate the following products without multiplying directly
$103 \times 105$
Show that :
$x+3$ is a factor of $69+11 x-x^{2}+x^{3}$.
$76 \times 82$
If $a+b+c=0,$ then the value of $a^{3}+b^{3}+c^{3}$ is equal to
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