Given that
$$P ( x ) = 125 x ^ { 3 } + 150 x ^ { 2 } + 55 x + 6$$
use the factor theorem to prove that ( \(5 x + 1\) ) is a factor of \(\mathrm { P } ( x )\). [0pt]
[2 marks]
13
Factorise \(\mathrm { P } ( x )\) completely.
13
Hence, prove that \(250 n ^ { 3 } + 300 n ^ { 2 } + 110 n + 12\) is a multiple of 12 when \(n\) is a positive whole number.