Discussion
If \((2x + 5y)^{2} - 5(2x + 5y) - 14 = (2x + 5y + p)(2x + 5y + q)\), then the value of \((p + q)\) is :
Answer: D
The value of \(p + q\) is \(-5\).
Put \(t = 2x + 5y\). The left side becomes a quadratic in t, which factorises:
\[ \begin{aligned} t^2 - 5t - 14 &= (t - 7)(t + 2) \\ p &= -7, \quad q = 2 \\ p + q &= -5 \end{aligned} \]
In \((t + p)(t + q)\) the sum p + q is the coefficient of t, here \(-5\). The product pq is \(-14\), which is the distractor, and 9 and 7 come from sign slips.
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