What am I doing wrong?

$x^2-5x+6$  and  $x^3-6x^2+11x+a$ have a common factor. Find the possible value of a.

The way I tried to solve it was.


$x^2-5x+6=(x-2)(x-3)$ so then $x=3$ or $x=2$ 

$f(3)=3^3-6\times 3^2+11\times3 +a=6+a=0 $
                                                                       $-6 $           $-6 $ 

$f(2)=2^3-6\times 2^2+11\times2 +a=6+a=0$
                                                                       $-6 $           $-6 $ 

So a = -6 but in my textbook, it says that it is incorrect and the actual answer is -66 or 18


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Kav10 Kav10
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