Question

what value of c makes $x^2 - 12x + c$ a perfect square trinomial?
-36
-24
24
36

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \(x^2 + bx + c=(x + \frac{b}{2})^2\), so \(c = (\frac{b}{2})^2\).

Step2: Identify \(b\) and calculate \(c\)

In \(x^2-12x + c\), \(b=-12\). Then \(\frac{b}{2}=\frac{-12}{2}=-6\), and \(c = (-6)^2 = 36\).

Answer:

36 (corresponding to the option "36")