Question

what value of c makes $x^2 + 6x + c$ a perfect square trinomial?
○ 3
○ 6
○ 9
○ 12

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \( (x + a)^2 = x^2 + 2ax + a^2 \). For the given trinomial \( x^2 + 6x + c \), compare with \( x^2 + 2ax + a^2 \). Here, \( 2a = 6 \).

Step2: Solve for a

From \( 2a = 6 \), divide both sides by 2: \( a = \frac{6}{2} = 3 \).

Step3: Find c (which is \( a^2 \))

Now, \( c = a^2 \). Substitute \( a = 3 \), so \( c = 3^2 = 9 \).

Answer:

9 (corresponding to the option "9")