Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the
trinomial.
-$$x ^ { 2 } + \frac { 4 } { 9 } x$$
A) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 2 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
B) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 9 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
C) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 4 } { 81 } = \left( x + \frac { 2 } { 9 } \right) ^ { 2 }$
D) $x ^ { 2 } + \frac { 4 } { 9 } x + \frac { 8 } { 81 } = \left( x + \frac { 4 } { 9 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

To form a perfect square trinomial from $x^2 + \frac{4}{9}x$, add $\left(\frac{1}{2} \cdot \frac{4}{9}\right)^2 = \left(\frac{2}{9}\right)^2 = \frac{4}{81}$. Factoring gives $\left(x + \frac{2}{9}\right)^2$.

Add the Proper Constant to the Binomial So That the Resulting