To complete the square for the polynomial \( m^2 - 2m + \), we need to find a number that makes it a perfect-square quadratic.
- Take the coefficient of the linear term, which is \(-2\).
- Divide it by \(2\): \[ \frac{-2}{2} = -1 \]
- Square that result: \[ (-1)^2 = 1 \]
Thus, the number that should be added to the polynomial to make it a perfect square is \(1\).
Therefore, we can write: \[ m^2 - 2m + 1 = (m - 1)^2 \]
So, the complete expression is: \[ m^2 - 2m + 1 \]
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