Question

PLEASE HELP. WILL GIVE BRAINLIEST

Answer 1

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.