If x – 1 is a factor of the polynomial f(x), then it must be true that f(1) = 0.
This means that when you substitute x = 1 into the polynomial, the result should be zero. This is a direct consequence of the Factor Theorem, which states that for any polynomial f(x), if (x – c) is a factor, then f(c) must equal zero.
Thus, in this case, since we know x – 1 is a factor, it follows that:
- f(1) = 0
Other values, such as f(0) or f(2), do not have a necessary relation to x – 1 being a factor. Only f(1) specifically must equal zero. This ensures that the polynomial can be factored as f(x) = (x – 1)g(x), where g(x) is another polynomial.