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The polynomial $x^{3} - 3 x^{2} - 9 x + c$ can be written in the form ${(x - a)}^{2} (x - b)$ , then $c =$

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answer is D.

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Detailed Solution

f (x) = x^{3} - 3 x^{2} - 9 x + c

$f^{1} (x) = 3 x^{2} - 6 x - 9 = 0$

$x^{2} - 2 x - 3 = 0$

$x^{2} - 3 x + x - 3 = 0$

$(x - 3) (x + 1) = 0$

$x = 3, - 1$

$f (3) = 27 - 27 - 27 + c = 0$

$c = 27$

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