(i)[2]
Use the factor theorem to show that, in fact, $(x + 2)$ is a factor of $x^4 + 2x^3 + 2x^2 - 12x - 32$.
(ii)[3]
Show that $\beta$ can be expressed in an equation of the form $x = \sqrt[3]{(p + qx)}$, and give the values of $p$ and $q$.
(iii)[3]
Use an iterative formula based on the equation in part (ii) to find $\beta$ correct to 4 significant figures. Record each iteration to 6 significant figures.
(c(ii))[3]
Show that $\beta$ matches an equation of the form $x = \sqrt[3]{(p + qx)}$, and give the values of $p$ and $q$.
(c(iii))[3]
Use an iterative formula based on the equation in part (ii) to find $\beta$ correct to $4$ significant figures. Record each iteration to $6$ significant figures.