One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.

Given:

The function is:

One factor of the given function is (x-3).

To find:

The x-intercepts and y-intercept.

Solution:

We have,

Spittle the middle term, so that we can get (x-3) as a factor.

Again splitting the middle term, we get

For x-intercepts, .

and and

and and

So, the x-intercepts are 1, 2 and 3.

Putting in the given function, we get

Therefore, the y-intercept of the function is -6.

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step-by-step explanation:

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step-by-step explanation:

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