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.

ANSWER

The y-intercept is (0,-12).

The x-intercepts are (1,0),(2,0) and (6,0).

EXPLANATION

The given polynomial function is

To find the y-intercept, we substitute x=0 to get:

This simplifies to

Therefore the y-intercept is (0,-12).

To find the x-intercepts we need to factor completely the given polynomial.

We use synthetic division to get the remaining factors. We carried the division in the attachment.

This implies that

The complete factorization is:

For x-intercepts, f(x)=0.

This implies that, x=1,2,6.

The x-intercepts are (1,0),(2,0) and (6,0).

a negative exponent is translated as follows:

so, we have

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