Question

one factor of the function f(x) = x^3 -7x^2+14x-8 is (x-4). describe how to find the x intercept and the y intercepts of the graph of f(x) without using technology.​

Answer 1

Answer:

(2 , 0)

(1 , 0)

(4 , 0)

(0, -8)

Step-by-step explanation:

f(x) = x³ -7x² + 14x - 8

The y intercept occurs when x = 0.

This means the first three terms all go to zero an the result is y = -8

As we are given one factor, (x - 4), we know that one zero will occur when this factor is zero

x - 4 = 0

x = 4

taking out the x - 4 term from the quadratic

x³ -7x² + 14x - 8 = (x² ± Cx + 2)(x - 4)

we can see that

2x ± 4Cx = 14x

±4C = 12

C = 12/±4 = ±3

also

±Cx² - 4x² = -7x²

±C - 4 = -7

so C = -3

(x² - 3x + 2)

(x - 2)(x - 1)

x = 2

x = 1