Discussion
One of the factors of \(p^{3}x + p^{2}(x - y) - p(y + z) - z\) is :
Answer: C
One factor is \(p^{2}x - py - z\).
Expand and group the terms so that a common factor of (p + 1) appears:
\[ \begin{aligned} & p^{3}x + p^{2}x - p^{2}y - py - pz - z \\ &= p^{2}x(p + 1) - py(p + 1) - z(p + 1) \\ &= (p + 1)(p^{2}x - py - z) \end{aligned} \]
The other options differ only in signs; multiplying any of them by (p + 1) does not give back the original expression, for example \(p^{2}x + py + z\) would produce +py and +z terms that are not there.
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