Decide whether the following statement is true or false. If false, tell why. Since $x-1$ is a factor of $f(x)=x^{6}-x^{4}+2 x^{2}-2$, we can conclude that $f(1)=0$. Is the statement true or false? A. The statement is true. B. The statement is false because since $x-1$ is a factor of $f(x)=x^{6}-x^{4}+2 x^{2}-2$, we can conclude that $f(0)=1$. C. The statement is false because since $x-1$ is a factor of $f(x)=x^{6}-x^{4}+2 x^{2}-2$, we can conclude that $f(-1)=0$.

Step 1 ：Decide whether the following statement is true or false. If false, tell why. Since \(x-1\) is a factor of \(f(x)=x^{6}-x^{4}+2 x^{2}-2\), we can conclude that \(f(1)=0\).

Step 2 ：The statement is saying that if \(x-1\) is a factor of \(f(x)\), then \(f(1)=0\). This is based on the factor theorem which states that a polynomial \(f(x)\) has a factor \((x - a)\) if and only if \(f(a) = 0\). So, to verify the statement, we need to substitute \(x=1\) into the function \(f(x)\) and check if the result is zero.

Step 3 ：Substitute \(x=1\) into the function \(f(x)\): \(f(1) = 1^{6}-1^{4}+2 \cdot 1^{2}-2 = 0\).

Step 4 ：Final Answer: The statement is \(\boxed{\text{true}}\).