Question

Since f(1)=0 for f(x)=x6−x4 2x2−2 , we can conclude that x−1 is a factor of f(x) .

Answer 1

Yes, x-1 is a factor of f(x).

Step-by-step explanation:

To prove that x-1 is a factor of f(x), we can use the factor theorem. According to the theorem, if f(a) = 0, then (x-a) is a factor of f(x). Given that f(1) = 0, we can conclude that x-1 is a factor of f(x).

In this case, when we substitute x=1 into the function f(x)=x⁶−x⁴ / 2x²−2, we get f(1) = 1⁶ - 1⁴ / 2*1² - 2 = 0. Therefore, by the factor theorem, x-1 is indeed a factor of f(x).

This conclusion allows us to express f(x) as (x-1) multiplied by another polynomial g(x). This simplifies the original function and provides valuable insight into its behavior and properties.