When we say that x – 1 is a factor of the polynomial f(x), it implies that f(1) = 0. This is a direct consequence of the Factor Theorem, which states that if x – c is a factor of f(x), then f(c) = 0.
Thus, if x – 1 is a factor, we can immediately conclude:
- f(1) = 0 – Since x = 1 is a root of the polynomial.
However, regarding the specific condition of f(0), it does not necessarily correlate with the factor x – 1. The value of f(0) could be any real number and is independent of whether x – 1 is a factor or not. The same holds true for f(-1).
In conclusion, the key point to remember if x – 1 is a factor of the polynomial f(x) is that f(1) = 0. The values of f(0) and f(-1) do not provide any necessary conditions related to this factor.