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

question 349

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

• A) \(\frac { 1 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }\)
• B) \(\frac { 1 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x + \frac { 1 } { 9 } \right) ^ { 2 }\)
• C) \(\frac { 4 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 4 } { 81 } = \left( x - \frac { 2 } { 9 } \right) ^ { 2 }\)
• D) \(\frac { 2 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 2 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }\) Solve the equation by completing the square.

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