Complete the square and factor the resulting perfect-square trinomial. $t ^ { 2 } + 8 t$
A)( t + 16 ) $2$
B)( t - 4 ) $2$
C)( t + 4 ) $2$
D)( t - 16 ) $2$

Question

Quizplus · Accepted Answer

To complete the square, we need to take half of the coefficient of the t-term, square it, and add it to the expression:
\begin{align*} t^2+8t &= t^2+8t+16-16 \ &= (t+4)^2-16 \end{align*}
The resulting perfect-square trinomial is $(t+4)^2$, which factors as $(t+4)(t+4)$ or $(t+4)^2$. Therefore, the answer is choice C.

Complete the Square and Factor the Resulting Perfect-Square Trinomial t2+8tt ^ { 2 } + 8 tt2+8t

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