Question

Suppose the polynomial function f has a zero at x = -3. Which of the following statements must be true?

a) (3,0) is an x-intercept of the graph of f.
b) (0,3) is a y-intercept of the graph of f.
c) x - 3 is a factor of f(x).
d) f(-3) = 0​

Answer 1

If a polynomial function f has a zero at x = -3, x - 3 is a factor of f(x).

Step-by-step explanation:

If a polynomial function f has a zero at x = -3, the statement that must be true is c) x - 3 is a factor of f(x).

1. To determine if x - 3 is a factor of f(x), we can use synthetic division. Divide f(x) by x - 3 and if the remainder is zero, then x - 3 is a factor of f(x).
2. For example, if f(x) = x^2 - 5x + 6, when we divide by x - 3, we get a remainder of zero. Therefore, x - 3 is a factor of f(x).

Answer 2

d) f(-3)=0

Step-by-step explanation:

Given that f is equal to zero at x=-3

So, f(-3)=0