Question

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

s2 + 14s +

Answer 1

To complete the square for the polynomial \( s^2 + 14s \), we want to find a number to add that will make it a perfect square.

1. Start with the coefficient of \( s \), which is 14.
2. Divide this coefficient by 2:
\[
\frac{14}{2} = 7
\]
3. Square this result:
\[
7^2 = 49
\]
4. Therefore, to complete the square, you need to add 49 to the polynomial.

So, the completed polynomial is:
\[
s^2 + 14s + 49
\]

This can be factored as:
\[
(s + 7)^2
\]

Thus, the number that makes the polynomial a perfect-square quadratic is **49**.