Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + \frac { 4 } { 3 } x$$
A) $\frac { 4 } { 9 } ; x ^ { 2 } + \frac { 4 } { 3 } x + \frac { 4 } { 9 } = \left( x + \frac { 2 } { 3 } \right) ^ { 2 }$
B) $\frac { 8 } { 9 } ; x ^ { 2 } + \frac { 4 } { 3 } x + \frac { 8 } { 9 } = \left( x + \frac { 4 } { 3 } \right) ^ { 2 }$
C) $\frac { 4 } { 3 } ; x ^ { 2 } + \frac { 4 } { 3 } x + \frac { 4 } { 3 } = \left( x + \frac { 2 } { 3 } \right) ^ { 2 }$
D) $\frac { 2 } { 9 } ; x ^ { 2 } + \frac { 4 } { 3 } x + \frac { 2 } { 9 } = \left( x + \frac { 2 } { 3 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

To make a perfect square trinomial, add $(\frac{b}{2})^2$, where $b = \frac{4}{3}$. Thus, $(\frac{4}{3} / 2)^2 = (\frac{2}{3})^2 = \frac{4}{9}$. The trinomial becomes $(x + \frac{2}{3})^2$.

Determine the Constant That Should Be Added to the Binomial x2+43xx ^ { 2 } + \frac { 4 } { 3 } xx2+34​x

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } + \frac { 4 } { 3 } x$