Complete the square and factor the resulting perfect-square trinomial. $8 t ^ { 2 } + 120 t$
A)( 8 t + $\frac { 225 } { 4 }$ ) $2$
B)( 8 t - $\frac { 15 } { 2 }$ ) $2$
C)( 8 t + $\frac { 15 } { 2 }$ ) $2$
D)( 8 t - $\frac { 225 } { 4 }$ ) $2$

Question

Quizplus · Accepted Answer

To complete the square, we need to add and subtract the square of half of the coefficient of the t term. 
\begin{align*}
8t^2 + 120t &= 8(t^2 + 15t) \
&= 8(t^2 + 15t + \frac{225}{4} - \frac{225}{4}) \
&= 8((t+\frac{15}{2})^2 - \frac{225}{4}) \
&= 8(t+\frac{15}{2})^2 - 900 \
&= 8(t+\frac{15}{2})^2 - (30)^2
\end{align*}

Therefore, the factorization is (8t + 15/2)(t + 15) and the best choice is C.

Complete the Square and Factor the Resulting Perfect-Square Trinomial 8t2+120t8 t ^ { 2 } + 120 t8t2+120t

Complete the Square and Factor the Resulting Perfect-Square Trinomial $8 t ^ { 2 } + 120 t$