State the degree of the following polynomial: $p(x) = 6 - 5x^3 + 4x^5 - 5x^2$.

Draw the graph of $p(x) = x^{2} + x - 12$ and find the zeros of this polynomial.

What must be added to the polynomial $p(x) = 6x^5 + 5x^4 + 11x^3 - 3x^2 + x + 1$ so that the resulting polynomial is exactly divisible by $3x^2 - 2x + 4$? (Hint: add $-r(x)$ to $p(x)$)

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

If the polynomial $p(x)$ is divided by $x^{2}+4x+2$, then the quotient polynomial $x^{2}-4x+14$ and the remainder polynomial $9x-13$ are obtained. Find the polynomial $p(x)$.

The number of real zeros of $y=p(x)$ is ........... in the given figure.