Factorise

$x^{3}+2 x^{2}-13 x+10$

Which of the following expressions is a polynomial, state the reason ? If an expression is polynomial, state whether it is a polynomial in one variable or not

$x^{2}-15 x+50$

If $x+y=12$ and $x y=27,$ find the value of $x^{3}+y^{3}$

By using the factor theorem, show that $(x+2)$ is a factor of the polynomial $6 x^{3}+19 x^{2}+16 x+4$ and then factorise $6 x^{3}+19 x^{2}+16 x+4$

Find the quotient and the remainder when $2 x^{2}-7 x-15$ is divided by

$2 x-3$