One factor of the function f(x) = x3 − 9x2 + 20x − 12 is (x − 6). describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. include all intercepts in your answer.

Step-by-step explanation:

Synthetic division (shown below) or polynomial long division can be used to factor the binomial (x-6) from the cubic. The remaining quadratic is ...

  (x^2 -3x +2)

and this can be factored as ...

  (x -1)(x -2)

So the factorization of f(x) is ...

  f(x) = (x -6)(x -2)(x -1)

The x-intercepts are the values of x that make these factors zero: {6, 2, 1}.

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The y-intercept is f(0) = -12. (It is the constant term, as all the variable terms are zero at f(0).)

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It is convenient to let technology create the diagram of synthetic division as shown here. The process is simple enough it is easily done by hand.

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