Factor the perfect square trinomial below. $\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }$
A) $\left( \frac { 7 } { 6 } x + \frac { 5 } { 4 } \right) ^ { 2 }$
B) $\left( - \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$
C) $\left( \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$
D) $\left( \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right)$
E) $\left( - \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

To factor a perfect square trinomial of the form $ax^{2}+bx+c$, we take half of the coefficient of the $x$ term ($\frac{b}{2}$), square it, and add/subtract it to/from the constant term ($c$). In this case, $\frac{b}{2}=\frac{35}{24}$, so $\left(\frac{5}{4}x+\frac{7}{6}\right)^2=\frac{25}{16}x^2+\frac{35}{12}x+\frac{49}{36}$. Therefore, the answer is (C).

Factor the Perfect Square Trinomial Below 2516x2+3512x+4936\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }1625​x2+1235​x+3649​

Factor the Perfect Square Trinomial Below $\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }$