Total number of polynomials of the form \( x^{3}+a x^{2}+b x+ \) \( c \) that are divisible by \...

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Total number of polynomials of the form \( x^{3}+a x^{2}+b x+ \) \( c \) that are divisible by \( x^{2}+1 \), where \( a, b, c \in\{1,2,3, \ldots \), \( 9,10\} \) is equal to
(A) 10
(B) 15
(C) 5
(D) 8
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