2012-II-03

Ans: C

\begin{array}{rcl} x^{2} + p & \equiv & (x + 2) (x + q) + 10 \\ x^{2} + p & \equiv & x^{2} + (2 + q) x + (2 q + 10) \end{array}

By comparing the coefficients of both sides, we have

$\begin{array}{rcl} 0 & = & 2 + q \\ q & = & - 2 \end{array}$

Also,

$\begin{array}{rcl} p & = & 2 q + 10 \\ = & 2 (- 2) + 10 \\ = & 6 \end{array}$

2012, HKDSE-MATH, Paper 2 Polynomials