$p$ and $q$ are the zeroes of a polynomial $2x^2+5x-4$. Without finding the actual values of $p$ and $q$, evaluate $\left(1-p\right)\left(1-q\right)$. Show your steps.

Two polynomials are shown in the graph below. Find the number of zeroes that are common to both polynomials. Explain your answer.

$\frac{x^2-3\sqrt{2}x+4}{x-\sqrt{2}}$;  $x\ne \sqrt{2}$

At how many points does the graph of the above expression intersect the $x$ axis? Show your work.

Write a quadratic polynomial whose sum of zeroes is less than that of polynomial 

Shown below is a part of the graph of a polynomial $h\left(x\right)$

On dividing $h\left(x\right)$ by which of the following, the remainder will be zero?

$\left(\mathrm{i}\right) \left(x-2\right)$

$\left(\mathrm{ii}\right) \left(x+2\right)$

$\left(\mathrm{iii}\right) \left(x-4\right)$

$\left(\mathrm{iv}\right) \left(x+4\right)$

Shown below are the parts of graphs of two polynomials, $g\left(x\right)$ and $h\left(x\right)$. When $h\left(x\right)$ is divided by $\left(x-3\right)$, the remainder is $k$

Which of these is true for the remainder when $g\left(x\right)$ is divided by $\left(x-3\right)$?

If $\alpha$ and $\beta$ are the zeroes of polynomial $x^2+8x+6$. Form a polynomial whose zeroes are $\alpha -\beta \text{and} \alpha +\beta$.