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Further Mathematics Paper 2, Nov/Dec. 2008  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 3

The remainder when the polynomial px4 + q3 – 8x2 + 6 is divided by (x2 - 1) is (2x + 1).  Find the values of the constants p and q.

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Observation

Most candidates performed poorly in this question. They were expected to obtain 2 equations in p and q by substituting the values x  =  ± 1 in the polynomial and then equate to the values of 2x + 1 when x  =  + 1.  The 2 equations are p + q = 5 and p-q = 1.  On solving simultaneously, p = 3 and q = 2.

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