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

Find the division of the following by synthetic division method: $p(x) = x^{4} + 1$ by $x + 1$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^{2} + 5\sqrt{2}x - 3$

Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the $x$-axis at only one point,it cannot be a quadratic polynomial.

Examine the validity of the following statement: $(x+3)$ is a factor of $(x^{2}+10x+21)$.

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=6, b=-7, c=-3$.