Question

Factor/Remainder Theorem - Let k be any number:
If f(k) ≠ 0, then k is ___________

Answer 1

If f(k) ≠ 0, then k is not a factor of the polynomial f(x).

Step-by-step explanation:

The question is asking about the Factor/Remainder Theorem. According to the theorem, if a number k is not a root of a polynomial function f(x) (i.e., f(k) ≠ 0), then k is not a factor of f(x).

For example, consider the polynomial f(x) = x^2 - 5x + 6. The roots of this polynomial are x = 2 and x = 3, which means f(2) = 0 and f(3) = 0. Therefore, 2 and 3 are factors of f(x). If we choose any other number, say k = 4, then f(4) ≠ 0 and 4 is not a factor of f(x).

In summary, if f(k) ≠ 0, then k is not a factor of the polynomial f(x).