Determine the Constant That Should Be Added to the Binomial $$x ^ { 2 } + \frac { 4 } { 9 } x$$

question 98

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.
- $$x ^ { 2 } + \frac { 4 } { 9 } x$$

• A) \(\frac { 4 } { 81 } ; x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }\)
• B) \(\frac { 2 } { 81 } ; x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 2 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }\)
• C) \(\frac { 8 } { 81 } ; x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 8 } { 81 } = \left( x + \frac { 4 } { 9 } \right) ^ { 2 }\)
• D) \(\frac { 4 } { 9 } ; x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 9 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }\)

---

Definitions:

Characteristic Pattern

A distinctive or regular arrangement of traits or features that is typical of an individual or process.

Personality

describes the individual differences in characteristic patterns of thinking, feeling, and behaving.

Environmental Stimuli

External factors or changes in the environment that can elicit a response from organisms.

Castration

The removal of the testicles in males or ovaries in females, often referred to in a metaphorical sense to denote the loss of power or vitality.