The degree of the polynomial $p(x) = x^2 - x^3 + x + 1$ is $\ldots \ldots \ldots . .$

Draw the graph of $p(x) = x^3 - 2x^2$ and find the zeros of this polynomial.

For each of the following,find a quadratic polynomial whose sum and product of the zeroes are as given respectively. Also,find the zeroes of these polynomials by factorisation.
Sum of zeroes $= -\frac{8}{3}$,Product of zeroes $= \frac{4}{3}$

The zeros of cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$; $a \neq 0, a, b, c, d \in R$ are $\alpha, \beta$ and $\gamma$; then $\alpha\beta + \beta\gamma + \gamma\alpha = \ldots$

Obtain the sum and the product of the zeros of the following quadratic polynomial without finding the zeros: $4x^{2} - 4x + 1$.

The degree of $p(x) = x^2(1 + x + x^2) + 5$ is.............