Question

If x3 + ax2 + 2x + a+4 is exactly divided by x+a , then the value of a is

Answer 1

Answer:

$the \: value \: of \: a \: is \: \frac{ - 4}{3}$

Step-by-step explanation:

$zero \: of \: (x + a )\: is \: - a \\ p(x) = {x}^{3} + {ax}^{2} + 2x + a + 4 \\ p( - a) = 0 \\ p( - a) = ({ -a )}^{3} + a {( - a)}^{2} +2a+ a + 4 \\ 0 = - {a}^{3} + {a}^{3} + 3a + 4 \\ 0 = 3a + 4 \\ a = \frac{ - 4}{3}$

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