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 158

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 , touches \(x\)-axis
• \(\sqrt { 3 }\), multiplicity 1 , crosses \(x\)-axis;
• \(- \sqrt { 3 }\), multiplicity 1 , crosses \(x\)-axis
• B) 0, multiplicity 4 , crosses \(x\)-axis;
• 3 , multiplicity 1 , crosses \(x\)-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

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Definitions:

Perceptual Set

A readiness to perceive certain aspects of available sensory data and ignore others, influenced by expectations.

Binocular Disparity

Binocular depth perception cue; the difference in images between the two eyes, which is greater for objects that are close and smaller for distant objects.

Texture Gradient

A depth cue in which the gradation of texture suggests distance; closer portions have detailed, finely textured patterns, while farther portions appear smoother.

Linear Perspective

A method in art and design that depicts objects and scenes as they appear to the eye with diminishing size and converging lines for depth and proportion.