What value of c makes x2 − 12x + c a perfect square trinomial?

−36
−24
24
36

1 answer

To determine the value of \( c \) that makes the expression \( x^2 - 12x + c \) a perfect square trinomial, we can use the formula for a perfect square trinomial, which is of the form \( (x - a)^2 = x^2 - 2ax + a^2 \).

In this case, we can identify the coefficient of \( x \) in the trinomial \( x^2 - 12x + c \) as \( -12 \), which corresponds to \( -2a \).

Setting this equal, we have:

\[ -2a = -12 \]

Solving for \( a \):

\[ 2a = 12 \ a = 6 \]

Next, to find \( c \), we need to determine \( a^2 \):

\[ c = a^2 = 6^2 = 36 \]

Thus, the value of \( c \) that makes \( x^2 - 12x + c \) a perfect square trinomial is:

\[ \boxed{36} \]