Discussion
Let A = \(3x^{2} - 8x + 11\), B = \(-2x^{2} + 12x\), C = \(-4x^{2} + 7\) and D = \(x^{2} - x - 11\).
If (A + B + C) - D = \(px^{2} + qx + r\), then the value of (p + q + r) is :
Answer: D
The value of \((p + q + r)\) is 30.
Add A, B and C term by term, then subtract D:
\[ \begin{aligned} A + B + C &= -3x^2 + 4x + 18 \\ (A + B + C) - D &= -4x^2 + 5x + 29 \end{aligned} \]
So p = -4, q = 5, r = 29, and p + q + r = 30. Forgetting to change the signs of D's terms when subtracting gives \(-2x^2 + 3x + 7\), a total of 8, and none of 27, 28 or 31 follows from these polynomials.
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