2011SP-II-04

Ans: A

\begin{array}{rcl} x^{2} + p (x + 5) + q & \equiv & (x - 2) (x + 5) \\ x^{2} + p x + (5 p + q) & \equiv & x^{2} + 3 x - 10 \end{array}

By comparing the coefficients of both sides, we have

${\begin{cases} p = 3 & \dots ① \\ 5 p + q = - 10 & \dots ② \end{cases}$

Sub. $①$ into $②$ , we have

$\begin{array}{rcl} 5 (3) + q & = & - 10 \\ q & = & - 25 \end{array}$

2011SP, HKDSE-MATH, Paper 2 Polynomials