1. The problem is to find the constant term that completes the polynomial $m^2 - 4m + \_$ to make it a perfect-square quadratic. 2. A perfect-square quadratic has the form $\left(m - a\right)^2 = m^2 - 2am + a^2$. 3. Here, the middle term is $-4m$, so $-2a = -4$ which gives $a = 2$. 4. The constant term to complete the square is $a^2 = 2^2 = 4$. 5. Therefore, the completed perfect-square quadratic is $m^2 - 4m + 4 = (m - 2)^2$. 6. This means the missing constant term is 4.