1.1. $f(x)={x}^{3}+p{x}^{2}+qx+6$ where $p$ and $q$ are constants.

Given that $(x-1)$ is a factor of $f(x)$ and that when $f(x)$ is divided by $(x+1)$ the remainder is 8

(i) show that $p=-2$

(ii) find the value of $q$

1.2. Hence, solve the equation $f(x)=0$