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

question 228

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.
- $$f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$$

• A) \(\frac { 1 } { 4 }\), multiplicity 4 , touches \(x\)-axis; 1 , multiplicity 5 , crosses \(x\)-axis
• B) \(\frac { 1 } { 4 }\), multiplicity 4 , crosses \(x\)-axis; 1 , multiplicity 5 , touches \(x\)-axis
• C) \(- \frac { 1 } { 4 }\), multiplicity 4 , touches \(x\)-axis; \(- 1\), multiplicity 5 , crosses \(x\)-axis
• D) \(- \frac { 1 } { 4 }\), multiplicity 4 , crosses \(x\)-axis; \(- 1\), multiplicity 5 , touches \(x\)-axis

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Definitions:

Grignard-Based Synthesis

A synthesis method involving the use of Grignard reagents to form carbon-carbon bonds.

1-Propylcyclohexanol

A chemical compound featuring a cyclohexanol moiety with a propyl group attached to the first carbon atom, involved in various organic syntheses.

Grignard-Based Synthesis

A chemical reaction involving the use of Grignard reagents to form carbon-carbon bonds, crucial for forming a wide array of complex molecules.

Methyl Isobutyrate

An ester formed from methanol and isobutyric acid, characterized by a fruity odor, commonly used in flavorings and fragrances.