Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } - 5 x$$
A) $\frac { 25 } { 4 } ; x ^ { 2 } - 5 x + \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$
B) $- \frac { 25 } { 4 } ; x ^ { 2 } - 5 x - \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$
C) $\frac { 5 } { 2 } ; x ^ { 2 } - 5 x + \frac { 5 } { 2 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$
D) $25 ; x ^ { 2 } - 5 x + 25 = ( x - 5 ) ^ { 2 }$

Question

Quizplus · Accepted Answer

To form a perfect square trinomial from $x^2 - 5x$, we need to add $\left(\frac{-5}{2}\right)^2 = \frac{25}{4}$. This results in $x^2 - 5x + \frac{25}{4}$, which factors to $\left(x - \frac{5}{2}\right)^2$.

Determine the Constant That Should Be Added to the Binomial x2−5xx ^ { 2 } - 5 xx2−5x

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } - 5 x$