If x – 4 is a factor of the polynomial f(x), then it must also be true that f(4) = 0.
This follows from the Factor Theorem, which states that a polynomial f(x) has a factor of the form x – c if and only if f(c) = 0. In this case, because x – 4 is a factor, substituting 4 into the polynomial should yield a result of 0.
Therefore, when you evaluate the polynomial at x = 4, the output must be 0. This is a crucial characteristic of polynomials and helps you find roots and factors more easily.