Question 1081854
Possible roots to try would be  -6,-4,-3,-2,-1,1,2,3,4,6,12 (Rational Roots Theorem).

<pre>
2   |    1   -6   9   4    -12
    |         2   -8  2     12
    |________________________________
        1    -4   1   6     0


3   |    1    -4    1     6
    |
    |          3    -3    -6
    |______________________________

         1    -1   -2     0

</pre>


Partial factorizing gives {{{f(x)=(x-2)(x-3)(x^2-x-2)}}}.


The quadratic factor breaks into f being
{{{f(x)=(x-2)(x-3)(x-2)(x+1)}}}
{{{highlight(f(x)=(x+1)(x-2)^2*(x-3))}}}


x-intercepts:
-1, 2, 3


y-intercept:
When x=0, y=-12.


Table of Signs:
Check inside each interval on x.
-
(infin, -1]
[-1, 2]
[2, 3]
[3, infinity)
-
You can determine the result in each interval on your own.



{{{graph(400,400,-5,5,-5,5,x^4-6x^3+9x^2+4x-12)}}}


{{{graph(400,400,-3,4,-5,5,x^4-6x^3+9x^2+4x-12)}}}


{{{graph(400,400,-12,12,-12,12,x^4-6x^3+9x^2+4x-12)}}}