Question

I require assistance, please ​

Answer 1

see explanation

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) =
`x^(4)` - 2x² + 1

So the term of highest degree is
`x^(4)`

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) =
`(-2)^(4)` - 2(- 2)² + 1 = 16 - 8 + 1 = 9 ≠ 0

Substitute x = - 1 into f(x)

f(- 1) =
`(-1)^(4)` - 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)

Answer 2

When x = -1, f(x) = 0 because

(-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0.