For the Polynomial, List Each Real Zero and Its Multiplicity $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

Multiple Choice

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
- $$f ( x ) = \frac { 1 } { 5 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x - 3 )$$

A) 0 , multiplicity 4 , touches $x$ -axis;
3 , multiplicity 1 , crosses $x$ -axis;
$\sqrt{3}$ , multiplicity 1 , crosses $x$ -axis;
$-\sqrt{3}$ , multiplicity 1 , crosses $x$ -axis

B) 0 , multiplicity 4 , crosses $\mathrm{x}$ -axis;
3 , multiplicity 1 , touches $x$ -axis

C) 0 , multiplicity 4 , crosses $x$ -axis;
3 , multiplicity 1 , touches $x$ -axis;
$\sqrt{3}$ , multiplicity 1 , touches $x$ -axis;
$-\sqrt{3}$ , multiplicity 1 , touches $x$ -axis

D) 0 , multiplicity 4 , touches $x$ -axis; 3 , multiplicity 1 , crosses $x$ -axis