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If (x + 1) is factor of ${ax}^{3} + {bx}^{2} + cx + d$ , then the condition is

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$a + b + c + d = 1$

$a + b = c + d$

$a + b + c + d = 0$

$a + c = b + d$

answer is B.

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Detailed Solution

$f (x) = a x^{2} + b x^{2} + c x + d f (- 1) = 0 \Rightarrow a {(- 1)}^{2} + b {(- 1)}^{2} + c (- 1) + d = 0 \Rightarrow - a + b - c + d = 0 \Rightarrow b + d = a + c$

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