Question 916833: Figuring out graphing of this polynomial:
f(x) = 12x^3 - 12x^2 - 24x
what I have so far:
I know I can factor it down, therefore 12x(x+1)(x-2)
and the x-int would be (-1,0),(2,0)
But why is (0,0) also a factor? I don't understand that.
also how would I find the degree and leading coefficient? very lost on that concept
And when I plug this poly into a graphing calculator it has a steepness and a lowness at two points. I am in precalculus so I don't know the finer details of graphing/derivatives and I must be able to do this freehand how would I know how far up to make the graph and how far low to make the graph?
Thank you
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! But WHY is (0,0) also a factor?
I just answered this question a few minutes ago.
LOOK at the factorization of f(x). You have the correct factorization. Three separate factors written in x.
The list of factors:
x
(x+1)
(x-2)
Each of those gives a x-intercept.
Note that one of the factors is x, so this means that when x=0, f is also zero, BECAUSE x IS ONE OF THE FACTORS OF THE FUNCTION f.
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