This question was reportedly attempted by majority of the candidates and their
performance was described as fair. Candidates were also reported to have
performed better in part (a) than in part (b) where majority of the candidates
were reported to have applied the appropriate rule of differentiation correctly.

In part (a), candidates were expected to apply the long division method to divide

f(x) = x3 + px2 – 10x + q by x2 + x – 5 to have:

x + (p – 1)

x2 + x – 6 x3 + px2 – 10x + q

x3 + x2 – 6x

(p - 1)x2 – 4x + q

__(p - 1)x2 + (p - 1)x – 6(p - 1)__

(-4 - (p - 1))x + q + 6 (p - 1)

Since x2 + x – 6 is a factor, then (-4 - (p - 1))x + q + 6(p - 1) = 0. i.e -4 - (p - 1) = 0 and q + 6(p - 1) = 0. This implied that p – 1 = -4 or p = -3 and q = -6(p-1) = -6(-3-1) = 24. The third factor was x + (p - 1) = x + (-3 - 1) = x – 4.