If $p(x) = x^{3} - 3x^{2} - x + 3$ is divided by $x - 1$,then the remainder is .............

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=6, b=-7, c=-3$.

Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients: $x^{2}-2x-8$.

Find the zeros of the following quadratic polynomial: $p(x) = 4x^2 - 256$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$5 t^{2}+12 t+7$