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If $(x + 2)$ $(x+2)$ is a factor of $x^{3} - 6 x^{2} + k x + 10$ $x^3-6x^2+kx+10$ , what is k?

1 Answer

Jan 30, 2017

The answer is $k = - 11$ $k=-11$

Explanation:

Let $f (x) = x^{3} - 6 x^{2} + k x + 10$ $f(x)=x^3-6x^2+kx+10$

If $(x + 2)$ $(x+2)$ is a factor

Then,

$f (- 2) = 0$ $f(-2)=0$

$f (- 2) = - 8 - 24 - 2 k + 10 = 0$ $f(-2)=-8-24-2k+10=0$

$2 k = - 22$ $2k=-22$

$k = - 11$ $k=-11$

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