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

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

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

The zero of the linear polynomial $p(x) = ax + b$ is $\ldots \ldots \ldots \ldots$ $(a, b \neq 0)$.

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= \frac{1}{4}$;
The product of the zeros $= -1$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$2x^2 + \frac{7}{2}x + \frac{3}{4}$