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

$x+1$

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 $6 x^{3}+19 x^{2}+16 x+4$

Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.

Factorise the following quadratic polynomials by splitting the middle term

$x^{2}-4 x-77$

In the polynomial $5 x^{3}-3 x^{2}+11 x-4,$ the coefficient of $x^{2}$ is……