APFIVE Interpreting a Polynomial Sign Chart
Based on the following sign chart for a polynomial function $$f(x)$$, all of the following statements are true except:
| Interval | Test Value | Sign of f(x) |
|---|---|---|
| (-∞, -2) | -3 | Negative |
| (-2, 0) | -1 | Positive |
| (0, 3) | 1 | Negative |
| (3, ∞) | 4 | Positive |
A
When solving a strict inequality such as $$f(x) > 0$$, the zeros of $$f(x)$$ should always be included in the solution.
B
Finding the zeros of the polynomial is the first step in solving the inequality.
C
The sign chart shows that the sign of $$f(x)$$ is consistent within the intervals between zeros.
D
The multiplicity of a zero determines whether $$f(x)$$ changes sign when passing through that zero.
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