Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + \frac { 1 } { 5 } x$$
A) $\frac { 1 } { 100 } ; x ^ { 2 } + \frac { 1 } { 5 } x + \frac { 1 } { 100 } = \left( x + \frac { 1 } { 10 } \right) ^ { 2 }$
B) $\frac { 1 } { 25 } ; x ^ { 2 } + \frac { 1 } { 5 } x + \frac { 1 } { 25 } = \left( x + \frac { 1 } { 5 } \right) ^ { 2 }$
C) $\frac { 1 } { 10 } ; x ^ { 2 } + \frac { 1 } { 5 } x + \frac { 1 } { 10 } = \left( x + \frac { 1 } { 5 } \right) ^ { 2 }$
D) $100 ; x ^ { 2 } + \frac { 1 } { 5 } x + 100 = ( x + 10 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

To form a perfect square trinomial from $x^2 + \frac{1}{5}x$, you add $\left(\frac{1}{2} \cdot \frac{1}{5}\right)^2 = \left(\frac{1}{10}\right)^2 = \frac{1}{100}$. Factoring the resulting trinomial gives $\left(x + \frac{1}{10}\right)^2$.

Determine the Constant That Should Be Added to the Binomial x2+15xx ^ { 2 } + \frac { 1 } { 5 } xx2+51​x

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } + \frac { 1 } { 5 } x$