what value of c makes x² - 12x + c a perfect square trinomial?\n-36\n-24\n24\n36

Explanation:

Step1: Recall the formula for perfect - square trinomial

A perfect - square trinomial of the form (x^{2}+bx + c) can be written as ((x + m)^{2}=x^{2}+2mx+m^{2}), where (b = 2m) and (c=m^{2}). In the given trinomial (x^{2}-12x + c), we have (b=-12).

Step2: Find the value of (m)

Since (b = 2m) and (b=-12), then (2m=-12), so (m=\frac{-12}{2}=-6).

Step3: Calculate the value of (c)

Since (c = m^{2}) and (m=-6), then (c=(-6)^{2}=36).

Answer:

D. 36