Answer
$x = -5$ has multiplicity 1 (odd).
The graph crosses the x-axis.
$x = -3$ has multiplicity 1 (odd).
The graph crosses the x-axis.
$x = 3$ has multiplicity 1 (odd).
The graph crosses the x-axis.
Work Step by Step
Multiplicity and x-Intercepts:
If $r$ is a zero of a polynomial f(x), then $(x-r)^{k}$ is a factor in the full factorization of f.
The exponent $k$ indicates the multiplicity of $r$.
If $r$ is a zero of even multiplicity, then the graph touches the x-axis and turns around at $r$.
If $r$ is a zero of odd multiplicity, then the graph crosses the x-axis at $r$.
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Begin factoring by factoring in pairs...
$f(x)=x^{2}(x+5)-9(x+5)$
... common factor: $(x+5)$...
$f(x)=(x+5)(x^{2}-9)$
... recognize a difference of squares $, x^{2}-3^{2}$
$f(x)=(x+5)(x+3)(x-3)$
Zeros: $-5,-5$ and $3.$
$x = -5$ has multiplicity 1 (odd).
The graph crosses the x-axis.
$x = -3$ has multiplicity 1 (odd).
The graph crosses the x-axis.
$x = 3$ has multiplicity 1 (odd).
The graph crosses the x-axis.