Determine the Constant That Should Be Added to the Binomial $$x ^ { 2 } + \frac { 1 } { 4 } x$$

question 13

Multiple Choice

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write
and factor the trinomial.
- $$x ^ { 2 } + \frac { 1 } { 4 } x$$

• A) \(64 ; x ^ { 2 } + \frac { 1 } { 4 } x + 64 = ( x + 8 ) ^ { 2 }\)
• B) \(\frac { 1 } { 8 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 8 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }\)
• C) \(\frac { 1 } { 64 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 64 } = \left( x + \frac { 1 } { 8 } \right) ^ { 2 }\)
• D) \(\frac { 1 } { 16 } ; x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 16 } = \left( x + \frac { 1 } { 4 } \right) ^ { 2 }\)

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Definitions:

Leon Festinger

A psychologist known for his theory of cognitive dissonance, which explores how people strive for internal consistency between their beliefs and behaviors.

Group Cohesion

The strength and solidarity of the bonds among group members, contributing to the group's unity, commitment, and capacity to act as a single entity.

Task Cohesion

The degree to which group members work together towards a common goal and the level of commitment to achieving that goal.

Entitativity

The degree to which a group is perceived as being a coherent, unified entity.