Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$

question 35

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

• A) \(x = 0\), multiplicity \(2 ; x = - 2\), multiplicity \(1 ; x = - 6\), multiplicity 1
• B) \(x = 2\), multiplicity \(2 ; x = 6\), multiplicity 2
• C) \(x = 0\), multiplicity \(2 ; x = 2\), multiplicity \(1 ; x = 6\), multiplicity 1
• D) \(x = - 2\), multiplicity \(2 ; x = - 6\), multiplicity 2
• E) \(x = 0\), multiplicity \(1 ; x = 2\), multiplicity \(1 ; x = - 2\), multiplicity \(1 ; x = 6\), multiplicity 1

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Definitions:

Direct Labor-Hours

The total hours worked directly on the production or manufacturing of goods, often used to allocate manufacturing overhead.

Denominator Activity

The level of activity used to compute the predetermined overhead rate.

Applied Factory Overhead

The portion of factory overhead costs assigned to each unit of production, based on an estimated or predetermined rate.

Electrical Motor

A device that converts electrical energy into mechanical energy, commonly used in appliances, industrial equipment, and vehicles.