PLEASE HELP. WILL GIVE BRAINLIEST 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.

x-intercepts = 1,2, and 4, y-intercept = -8

Step-by-step explanation:

x^3 - 7x^2 - 14x - 8 in factored form is equal to (x-1)(x-2)(x-4).

Solving for x-intercepts:

We are actually able to solve for all x-intercepts without the given factor. But since we are given one of the factors, our job becomes much easier.Using synthetic division, or long division, we factor out the x-intercept 4. Which leaves us with the polynomial x^2 - 3x + 2. From here we can separate the polynomial into two binomials.x^2 - 3x + 2 = (x-1)(x-2). Giving us all 3 x-intercepts.Using Descartes' rules we can identify before even starting the problem how many real x-intercepts there are (Not needed for this problem).

Solving for y-intercept:

The y-intercept is always the coefficient that does not have any assigned x-variables.The coefficient is -8, thus the y-intercept.If unsure of the y-intercept, you can always plug in x = 0. Solving for the y-intercept will give you the value of f(0).If there is no coefficient, the y-intercept is equal to zero.