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

Question

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

Jacqueline Cortes · Accepted Answer

Final Answer : C, Explanation :  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).

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