The degree of the polynomial $p(x) = 3x - x^4 + x^2 + 2x^3 + 7$ is ..........

Given that $\sqrt{2}$ is a zero of the cubic polynomial $6x^{3}+\sqrt{2}x^{2}-10x-4\sqrt{2}$,find its other two zeroes.

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

Identify the type of the following polynomial based on its degree: $p(x) = (x - 15)(x + 15)$

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: $4u^{2} + 8u$.

The product of the zeros of $p(x) = 4x^{2} + 12x + 5$ is..........