One factor of the function f(x) = x3 − 7x2 + 14x − 8 is (x − 4). 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.

The y-intercept is (0, -8).

The x-intercepts are (1, 0), (2, 0), and (4, 0).

Step-by-step explanation:

We are given the function:

And one of its factors:

And we want to find the x-intercepts and the y-intercept.

First, the y-intercept is simply when the function crosses the y-axis. So, it occurs when x = 0. Therefore, the y-intercept is:

The y-intercept is (0, -8).

To find the x-intercept(s), we will use our given factor. Using synthetic division, find the depressed polynomial. This is shown below. Remember that we can use synthetic division when dividing by a binomial in the form (x - a). In this case, a = 4. Thus:

This can then be factored:

x-intercepts occur when y = 0. Thus:

By the Zero Product Property:

Solve each equation.

Hence, our x-intercepts are (1, 0), (2, 0), and (4, 0).

all it means is function 3