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

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

Find the zeroes of the following polynomial by the factorization method and verify the relationship between the zeroes and the coefficients of the polynomial:
$3x^2 + 4x - 4$

For the given sum and product of zeroes,find a quadratic polynomial. Also,find the zeroes of this polynomial by factorisation:
Sum of zeroes = $\frac{-3}{2 \sqrt{5}}$,Product of zeroes = $-\frac{1}{2}$

Obtain the sum and the product of the zeros of the following quadratic polynomial without finding the zeros: $x^{2}-7x+10$.

There are $x^{2}-2$ students in the class. $x^{3}-3x^{2}+5x-3$ chocolates are distributed between them. Each student should get the maximum possible number of chocolates. Find the number of chocolates received by each student and the number of chocolates left undistributed $(x \in N)$.