SOLUTION: Given the polynomial f(x)= x^4 -6x^3 +9x^2 +4x -12 , (I) factorize f(x) completely and hence find the x and y axes intercepts (II) state the x coordinates where the graph of

Question 1081854: Given the polynomial f(x)= x^4 -6x^3 +9x^2 +4x -12 ,
(I) factorize f(x) completely and hence find the x and y axes intercepts
(II) state the x coordinates where the graph of y=f(x) cuts the x-axis and where it touches the x-axis
(III) draw a sign diagram for f(x)
(IV) discuss the behaviour of f(x) as x = ∞ and as x = -∞
(V) sketch the graph of y=f(x), using the information obtained above.
Answer by josgarithmetic(39626) (Show Source): You can put this solution on YOUR website!
Possible roots to try would be -6,-4,-3,-2,-1,1,2,3,4,6,12 (Rational Roots Theorem).

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

Partial factorizing gives .

The quadratic factor breaks into f being

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.

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