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

question 208

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