To determine the components (factors) of the given polynomial expression, we first simplify it and then apply the Factor Theorem.

Simplify the Polynomial Expression

The given expression is $P(x) = (x^6-x^4-x^5-x^4+x^2-4)$. Combine like terms:

$P(x) = x^6 - x^5 - (x^4 + x^4) + x^2 - 4$

$P(x) = x^6 - x^5 - 2x^4 + x^2 - 4$

Test for Component (x-1)

According to the Factor Theorem, $(x-a)$ is a factor of a polynomial $P(x)$ if $P(a) = 0$. For $(x-1)$, we test $P(1)$.

Substitute $x=1$ into the simplified polynomial:

$P(1) = (1)^6 - (1)^5 - 2(1)^4 + (1)^2 - 4$

$P(1) = 1 - 1 - 2(1) + 1 - 4$

$P(1) = 1 - 1 - 2 + 1 - 4$

$P(1) = -5$

Since $P(1) \neq 0$, $(x-1)$ is not a component of the polynomial.

Test for Component (x+1)

For $(x+1)$, which is $(x-(-1))$, we test $P(-1)$.

Substitute $x=-1$ into the simplified polynomial:

$P(-1) = (-1)^6 - (-1)^5 - 2(-1)^4 + (-1)^2 - 4$

$P(-1) = 1 - (-1) - 2(1) + 1 - 4$

$P(-1) = 1 + 1 - 2 + 1 - 4$

$P(-1) = 2 - 2 + 1 - 4$

$P(-1) = -3$

Since $P(-1) \neq 0$, $(x+1)$ is not a component of the polynomial.

Conclusion on Components

Both tests show that neither $(x-1)$ nor $(x+1)$ result in a value of 0 when substituted into the polynomial. Therefore, neither $(x-1)$ nor $(x+1)$ are components of the given polynomial expression.