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(x² +9) and g(x) are factors of f(x).
That is, (x² +9)(g(x)) = f(x).

The roots of (x² +9) are roots of f(x). They are 3i and -3i.

The factor (x² +9) has degree 2, so f(x) has degree at least 2.

We cannot say anything about the x- or y-intercepts based on this information.

Imaginary roots usually come in even numbers (2, 4, etc.) for the polynomials we study. The information given here does not support the idea of 3 imaginary roots for f(x).