One factor of the function f (x) = x^3 - 7x^2 + 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: 1,2,4

y-intercept: - 8

Step-by-step explanation:

f (x) = x³ - 7x² + 14x - 8

y-intercept is when x = 0

y = 0 - 0 + 0 - 8

y-intercept is - 8

x-intercept is when y = 0

x³ - 7x² + 14x - 8 = 0

(x³ - 8) + (-7x² + 14x) = 0

[x³ - 2³] - 7x (x - 2) = 0

[ (x - 2) (x² + x (2) + 2²] - 7x (x - 2) = 0

(x - 2) (x² + 2x + 4) - 7x (x - 2) = 0

(x - 2) (x² + 2x + 4 - 7x) = 0

(x - 2) (x² - 5x + 4) = 0

(x - 2) [x² - 4x - x + 4] = 0

(x - 2) [x (x - 4) - 1 (x - 4) ] = 0

(x - 2) (x - 4) (x - 1) = 0

x = 2, 4, 1 are the x-intercepts

Step-by-step explanation:

divide f (x) by x-4. That gives you

f (x) = (x-4) (x^2-3x+2) = (x-4) (x-1) (x-2)

Now you know the x-intercepts. To find the y-intercept, plug in x=0

f (0) = (-4) (-1) (-2) = - 8