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 $x = -2$.

Find a quadratic polynomial,the sum and product of whose zeroes are $\sqrt{2}$ and $-\frac{3}{2},$ respectively. Also,find its zeroes.

If the product of the zeros of $p(x) = ax^{2} - 6x - 6$ is $4$,then $a = $ ............

Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

If $x^{2}+6x+10$ is divided by $x+2$,then the remainder is..........

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^2 - 3x - 1$