Answer: The correct option is (C) 3.
Step-by-step explanation: Given that Sienna is solving the quadratic equation by completing the square as follows:
\(3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow a(x^2+3x)=4.\)
We are given to find the find the value of a.
We can see that in the second step of Sienna's solution, 3 is common in both the terms, \(3x2\) and \(9x.\)
So, she took 3 out and then in the third step, the expression within the bracket remais \(x^2+3x.\)
Therefore, the complete steps are as follows:
\(3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow 3(x^2+3x)=4.\)
Hence, the value of a is 3.
Thus, (C) is the correct option.
