6. \(\mathrm { f } ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } - 1\)
a. (i) Show that ( \(2 x - 1\) ) is a factor of \(\mathrm { f } ( x )\).
(ii) Express \(\mathrm { f } ( x )\) in the form \(( 2 x - 1 ) ( x + a ) ^ { 2 }\) where \(a\) is an integer. Using the answer to part a) (ii)
b. show that the equation \(2 p ^ { 6 } + 3 p ^ { 4 } - 1\) has exactly two real solutions and state the values of these roots.
c. deduce the number of real solutions, for \(5 \pi \leq \theta \leq 8 \pi\), to the equation $$2 \cos ^ { 3 } \theta + 3 \cos ^ { 2 } \theta - 1 = 0$$