Answer
x = $-5$, multiplicity $1$, crosses the x-axis
x = $5$, multiplicity $2$, touches the x-axis and turns
Work Step by Step
Multiplicity and x-intercepts (page 354):
If $(x-r)$ appears k times in a full factorization of f(x),
then r is a zero with multiplicity k.
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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Factor the expression of f(x):
$ f(x)=x^{3}-5x^{2}-25x+125\qquad$ ... factor in pairs
$f(x)=x^{2}(x-5)-25(x-5)$
$ f(x)=(x-5)(x^{2}-25)\qquad$
... recognize a difference of squares
$f(x)=(x-5)(x-5)(x+5)$
$f(x)=(x-5)^{2}(x+5)$
Zeros:
x = $-5$, multiplicity $1$, (odd), crosses the x-axis
x = $5$ multiplicity $2$, (even), touches the x-axis and turns
