For the polynomial

$\frac{x^{3}+2 x+1}{5}-\frac{7}{2} x^{2}-x^{6},$ write

$(i)$ the degree of the polynomial

$(ii)$ the coefficient of $x^{3}$

$(iii)$ the coefficient of $x^{6}$

$(iv)$ the constant term

Find $p(1), p(2)$ and $p(4)$ for each of the following polynomials

$p(t)=t^{2}-6 t+8$

Factorise $: x^{3}-125$

Evaluate

$77 \times 83$

If $p(3)=0$ for polynomial $p(x),$ state one factor of $p(x)$