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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​

User KKRocks
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2 Answers

1 vote

Final answer:

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).

User Yang Bo
by
8.3k points
4 votes

Answer:

d) f(-3)=0

Step-by-step explanation:

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

So, f(-3)=0

User Jordan Sitkin
by
8.9k points

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