what value of c makes $x^{2}-24x + c$ a perfect square trinomial?\n-144\n-48\n48\n144

Explanation:

Step1: Recall the formula for perfect - square trinomial

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

Step2: Identify the value of (b)

In the given expression (x^{2}-24x + c), (b=-24).

Step3: Calculate the value of (c)

Substitute (b = - 24) into the formula (c=\left(\frac{b}{2}\right)^{2}). We have (c=\left(\frac{-24}{2}\right)^{2}=(-12)^{2}=144).

Answer:

D. 144