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

Question

y2 + 22y +

Answer 1

To complete the square for the polynomial \(y^2 + 22y\), we need to add a specific number that makes it a perfect-square quadratic.

1. Take the coefficient of \(y\), which is 22.
2. Divide it by 2 to get 11.
3. Square that result: \(11^2 = 121\).

Now, we can rewrite the expression by adding \(121\): \[ y^2 + 22y + 121 \]

So, the number that makes the polynomial a perfect-square quadratic is 121.

The completed square form of the polynomial is: \[ (y + 11)^2 \]