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

Question

k2 − 30k +

Answer 1

To complete the square for the quadratic polynomial \( k^2 - 30k \), we follow these steps:

1. Take the coefficient of \( k \), which is \(-30\).
2. Divide it by 2: \(-30 / 2 = -15\).
3. Square the result: \((-15)^2 = 225\).

Now, we fill in the blank:

\[ k^2 - 30k + 225 \]

Therefore, the number that makes the polynomial a perfect-square quadratic is \( 225 \).

The completed square form of the polynomial would then be:

\[ (k - 15)^2 \]