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one factor of the function f(x) = x^3 - 9x^2 + 20x - 12 is (x-6). describe how to find the x-intercepts and the y-intercepts of the graph of f(x) without using any technology. show your work and include all intercepts in your answer.

x-intercepts are points of the form (x, 0), and y-intercepts are points of the form (0, y).

You find the x-intercepts by solving for x such that y = f(x) = 0:

You know x - 6 is a factor of f(x), which means x = 6 is a solution to the above equation, and that means that (6, 0) is one x-intercept.

You can find the other two by dividing f(x) by x - 6 (i.e. further factorizing f(x)).

So we have

and this means the x-intercepts are (6, 0), (2, 0) and (1, 0).

The y-intercept is easier to find; set x = 0, then solve for y = f(0):

and so the y-intercept is (0, -12).