If $p(x)=x^{4}-2 x^{3}+3 x^{2}-a x+3 a-7$ is divided by $(x+1),$ then the remainder is $19 .$ Find the value of a. Also, find the remainder, when $p(x)$ is divided by $(x+2)$

Evaluate the following products without multiplying directly

$103 \times 105$

Verify whether $2$ and $5$ are zeros of the polynomial $x^{2}-2 x-15$ or not.

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

From the following polynomials find out which of them has $(x+1)$ as a factor

$6 x^{3}+11 x^{2}-5 x-12$