When x = -1, f(x) = 0 because
(-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0.
Answer:
see explanation
Step-by-step explanation:
In order to determine the end behaviour, we only need to look at the term of highest degree, that is the leading term in standard form.
Given
f(x) = [tex]x^{4}[/tex] - 2x² + 1
So the term of highest degree is [tex]x^{4}[/tex]
Which is of even degree with positive coefficient
As a result the end behaviour is
As x approaches positive infinity, f(x) approaches positive infinity
As x approaches negative infinity, f(x) approaches positive infinity
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Substitute x = - 2 into f(x)
f(- 2) = [tex](-2)^{4}[/tex] - 2(- 2)² + 1 = 16 - 8 + 1 = 9 ≠ 0
Substitute x = - 1 into f(x)
f(- 1) = [tex](-1)^{4}[/tex] - 2(- 1)² + 1 = 1 - 2 + 1 = 0
Thus x = - 1 is a root of f(x) and (x + 1) is a factor of f(x)
