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

Question

y2 − 10y +

Answer 1

To complete the square for the polynomial \( y^2 - 10y \), we want to turn it into the form \( (y - a)^2 \).

1. Start with the coefficient of the linear term, which is \(-10\).
2. Divide this coefficient by 2: \( \frac{-10}{2} = -5 \).
3. Square the result: \( (-5)^2 = 25 \).

Now, we can rewrite the polynomial as:

\[ y^2 - 10y + 25 \]

The expression \( y^2 - 10y + 25 \) is a perfect square:

\[ (y - 5)^2 \]

Thus, the number that completes the square is 25.