Final answer:
To make x² + 12x a perfect square trinomial, we need to add (half the coefficient of x) squared, which is 36. This perfect square trinomial would be x² + 12x + 36, or (x + 6)².
Step-by-step explanation:
To make the expression x² + 12x a perfect square trinomial, we need to add the square of half the coefficient of x. The coefficient of x is 12, so half of this is 6. Therefore, we need to add 6², which is 36, to the expression.
The correct answer is not listed in the options, so we might be seeing a typographical error. If the original intent was to find (6²), which is 36 but instead, 144 is mentioned, it's important to note that 144 is (12²). Putting this into context, if we aim to form a perfect square trinomial by adding (6²), which is indeed 36, we would complete the expression as (x + 6)² = x² + 12x + 36.
The correct added term is 36 to get the perfect square trinomial x² + 12x + 36, which factorizes to (x + 6)².