The graph of $p(x) = x^2 - 9$ intersects the $X$-axis in .......... distinct points.

Prove that $1/2, 1$ and $-2$ are the zeros of the cubic polynomial $p(x) = 2x^3 + x^2 - 5x + 2$. Also,verify the relationship between the zeros and the coefficients.

For $p(x) = 3x^3 + 2x^2 + 7x + 8$,$p(-1) = \dots$

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

Obtain the value of the following polynomial at the given values of $x$: $p(x) = 10 - 5x + 3x^2 - x^3$; at $x = 2$ and $x = -2$.

Obtain the sum and the product of the zeros of the quadratic polynomial $6x^{2} - 7x - 3$ without finding the zeros.