Discussion
If \(A = -2x^{2} + 12x\), \(B = 11 - 8x + 3x^{2}\), \(C = 17 - 4x^{2}\) and \(D = x^{2} - x - 3\), then what is the sum of the co-efficients of \(x^{2}\) and x in \((A + B + C - D)\) ?
Answer: C
The sum of the coefficients is 1.
Collect the x2 and x terms, remembering that subtracting D changes the sign of each of its terms:
\[ \begin{aligned} x^{2}:\ -2 + 3 - 4 - 1 &= -4 \\ x:\ 12 - 8 + 0 + 1 &= 5 \\ -4 + 5 &= 1 \end{aligned} \]
The usual slip is to change the sign of only the first term of D. Every term of D must change sign, which is what turns its -x into +x and gives -4 and 5; -1 and 3 come from such sign errors.
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