To complete the square for the quadratic expression \( p^2 - 8p \), we need to add a specific value to make it a perfect-square polynomial.
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Start with the polynomial: \[ p^2 - 8p \]
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To complete the square, we take the coefficient of \( p \) (which is \(-8\)), divide it by 2, and then square it: \[ \left( \frac{-8}{2} \right)^2 = (-4)^2 = 16 \]
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Now, we add this value (16) to the expression: \[ p^2 - 8p + 16 \]
Thus, the number that makes the polynomial a perfect-square quadratic is \( \boxed{16} \).
The complete expression is: \[ p^2 - 8p + 16 = (p - 4)^2 \]
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