Question

x² + □x + 36

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial is of the form \(x^{2}+2abx + b^{2}=(x + b)^{2}\) or \(x^{2}-2abx + b^{2}=(x - b)^{2}\). Here, the constant term is \(36\), so we find \(b\) such that \(b^{2}=36\). Solving \(b^{2}=36\), we get \(b = 6\) or \(b=- 6\).

Step2: Calculate the middle term coefficient

Using the formula for the middle term, \(2ab\) (or \(- 2ab\)). For \(a = 1\) (coefficient of \(x^{2}\)) and \(b = 6\), the middle term is \(2\times1\times6x=12x\). For \(b=-6\), the middle term is \(2\times1\times(-6)x=- 12x\). Since the problem is likely looking for the positive case (or the common case), the middle term coefficient is \(12\) (or \(-12\), but usually \(12\) for \(x^{2}+12x + 36=(x + 6)^{2}\)).

Answer:

\(12\) (or \(-12\), but \(12\) is the more common positive case for the trinomial \(x^{2}+12x + 36=(x + 6)^{2}\))