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 gra
ph of f(x) without using technology.
1 answer:
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
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