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$(3 x+7)(-3 x+7)$

By using the factor theorem, show that $(x-3)$ is a factor of the polynomial $12 x^{3}-31 x^{2}-18 x+9$ and then factorise $12 x^{3}-31 x^{2}-18 x+9$

Using suitable identity, evaluate the following:

$101 \times 102$

Factorise :

$a^{3}-2 \sqrt{2} b^{3}$

Dividing $x^{3}+125$ by $(x-5),$ the remainder is $\ldots \ldots \ldots .$

Factorise the following quadratic polynomials by splitting the middle term

$x^{2}-3 x-40$