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

Question

s2 − 15s +

Answer 1

To complete the square for the quadratic polynomial \( s^2 - 15s \), we need to find the value that makes it a perfect square.

1. Start with the coefficient of \( s \), which is -15.
2. Take half of this coefficient: \( \frac{-15}{2} = -\frac{15}{2} \).
3. Square that result: \[ \left(-\frac{15}{2}\right)^2 = \frac{225}{4} \]

Now, we can fill in the blank:

The perfect square form of the polynomial \( s^2 - 15s + \frac{225}{4} \) is:

\[ \left(s - \frac{15}{2}\right)^2 \]

So, you need to add \( \frac{225}{4} \) to make \( s^2 - 15s \) a perfect-square quadratic.