Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

Question

r2 − 18r +

Answer 1

To complete the square for the quadratic \( r^2 - 18r \), we need to find a number that makes the expression a perfect square.

1. Take the coefficient of the linear term, which is \(-18\).
2. Divide it by 2: \[ \frac{-18}{2} = -9 \]
3. Square that result: \[ (-9)^2 = 81 \]

Now we add 81 to the polynomial to form a perfect square: \[ r^2 - 18r + 81 \]

Thus, the complete expression is: \[ r^2 - 18r + 81 = (r - 9)^2 \]

So, the number that makes the polynomial a perfect-square quadratic is 81.