If $p(x) = x^{3} - 3x^{2} - x + 3$ is divided by $x - 1$,then the remainder is .............

$P(x) = 4x^{3} + 3x^{2} + 2x + 1$ is a $\ldots$ polynomial.

Verify that $3$ is a zero of the linear polynomial $p(x) = 4x - 12$.

Answer the following and justify: If on division of a non-zero polynomial $p(x)$ by a polynomial $g(x)$,the remainder is zero,what is the relation between the degrees of $p(x)$ and $g(x)$?

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

The value of $p(x) = 2x^{4} - 3x^{3} + 7x + 5$ at $x = -2$ is $\ldots \ldots \ldots \ldots$