It is given that
$$P ( x ) = 4 x ^ { 3 } + 8 x ^ { 2 } + 11 x + 4$$
Use the factor theorem to show that \(( 2 x + 1 )\) is a factor of \(\mathrm { P } ( x )\)
13
Express \(\mathrm { P } ( x )\) in the form
$$\mathrm { P } ( x ) = ( 2 x + 1 ) \left( a x ^ { 2 } + b x + c \right)$$
where \(a\), \(b\) and \(c\) are constants to be found.
13
Given that \(n\) is a positive integer, use your answer to part (b) to explain why \(4 n ^ { 3 } + 8 n ^ { 2 } + 11 n + 4\) is never prime. [0pt]
[2 marks]