what value of c makes x² + 6x + c a perfect square trinomial?\n3\n6\n9\n12

Explanation:

Step1: Recall the formula

For a perfect - square trinomial of the form (x^{2}+bx + c), (c=\left(\frac{b}{2}\right)^{2}).

Step2: Identify the value of b

In the given trinomial (x^{2}+6x + c), (b = 6).

Step3: Calculate c

Substitute (b = 6) into the formula (c=\left(\frac{b}{2}\right)^{2}), we get (c=\left(\frac{6}{2}\right)^{2}=3^{2}=9).

Answer:

C. 9