If \( (x+1) \) and \( (x-1) \) are the factors of \( a x^{3}+b x^{2} \) \( +c x+d \), then which...

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If \( (x+1) \) and \( (x-1) \) are the factors of \( a x^{3}+b x^{2} \) \( +c x+d \), then which of the following is true?
(a) \( a+b=0 \)
(b) \( b+c=0 \)
(c) \( b+d=0 \)
(d) \( a+c=0 \)
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