You are given that \(\mathrm { f } ( x ) = ( x + 1 ) ( x - 2 ) ( x - 4 )\).
(A) Show that \(\mathrm { f } ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 2 x + 8\).
(B) Sketch the graph of \(y = \mathrm { f } ( x )\).
(C) The graph of \(y = \mathrm { f } ( x )\) is translated by \(\binom { 3 } { 0 }\).
State an equation for the resulting graph. You need not simplify your answer.
Find the coordinates of the point at which the resulting graph crosses the \(y\)-axis.
Show that 3 is a root of \(x ^ { 3 } - 5 x ^ { 2 } + 2 x + 8 = - 4\). Hence solve this equation completely, giving the other roots in surd form.