The cubic polynomial \(3{x^3} + p{x^2} + qx - 2\) has a factor \((x + 2)\) and leaves a remainder 4 when divided by \((x + 1)\). Find the value of p and the value of q.

\(f( - 2) = 0{\text{ }}( \Rightarrow  - 24 + 4p - 2q - 2 = 0)\)     M1

\(f( - 1) = 4{\text{ }}( \Rightarrow  - 3 + p - q - 2 = 4)\)     M1

Note:     In each case award the M marks if correct substitution attempted and right-hand side correct.

attempt to solve simultaneously \((2p - q = 13,{\text{ }}p - q = 9)\)     M1

\(p = 4\)     A1

\(q =  - 5\)     A1

[5 marks]

Many candidates scored full marks on what was thought to be an easy first question. However, a number of candidates wrote down two correct equations but proceeded to make algebraic errors and thus found incorrect values for p and q. A small number also attempted to answer this question using long division, but fully correct answers using this technique were rarely seen.