Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.
-Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $t ^ { 2 } - \frac { 14 } { 3 } t + n$
A) $n = \frac { 49 } { 9 } ; \left( t + \frac { 7 } { 3 } \right) ^ { 2 }$
B) $n = \frac { 49 } { 9 } ; \left( t - \frac { 7 } { 3 } \right) ^ { 2 }$
C) $n = \frac { 196 } { 9 } ; \left( t - \frac { 49 } { 3 } \right) ^ { 2 }$
D) $n = \frac { 98 } { 9 } ; \left( t - \frac { 98 } { 9 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

For a trinomial to be a perfect square, it must be in the form $(x \pm a)^2 = x^2 \pm 2ax + a^2$. Here, $a = \frac{7}{3}$ because $2 \cdot \frac{7}{3} = \frac{14}{3}$, and $n = (\frac{7}{3})^2 = \frac{49}{9}$. The correct factorization is $\left(t - \frac{7}{3}\right)^2$.

Find the Value of N So That the Expression Is t2−143t+nt ^ { 2 } - \frac { 14 } { 3 } t + nt2−314​t+n

Find the Value of N So That the Expression Is $t ^ { 2 } - \frac { 14 } { 3 } t + n$