When we say that x – 8 is a factor of f(x), we can apply the Factor Theorem, which states that if a polynomial f(x) has a factor of the form x – c, then f(c) = 0. In this case, we have c = 8.
This means that if x – 8 is a factor of f(x), then substituting 8 into the function should yield a result of zero. Therefore, we can conclude:
- f(8) = 0
This is essential because it confirms that 8 is a root of the polynomial function f(x). So, whenever you have a factor, remember to substitute the corresponding value into the function.