what value of c makes $x^{2}+6x + c$ a perfect square trinomial?\n3\n6\n9\n12

Explanation:

Step1: Recall the perfect - square trinomial formula

A perfect - square trinomial of the form (x^{2}+bx + c) can be written as ((x + m)^{2}=x^{2}+2mx+m^{2}). In the given trinomial (x^{2}+6x + c), we have (b = 6). Comparing (x^{2}+bx + c) with (x^{2}+2mx+m^{2}), we know that (b = 2m).

Step2: Find the value of (m)

Since (b = 6) and (b = 2m), we solve the equation (6=2m) for (m). Dividing both sides by 2, we get (m=\frac{6}{2}=3).

Step3: Find the value of (c)

Since (c=m^{2}) and (m = 3), then (c=3^{2}=9).

Answer:

C. 9