Let \( a, b, c, d \) and \( p \) be integers such that \( p \neq 0 ...

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Let \( a, b, c, d \) and \( p \) be integers such that \( p \neq 0 \). If \( x+p \) is a factor of \( a x^{3}+b x^{2}+c x+d \), then
(a) \( p \mid d \)
(b) \( p^{2} \mid(p c-d) \)
(c) \( d=0 \Rightarrow p \) is a root of \( a x^{2}-b x+c=0 \)
(d) none of these.
(W)
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