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