Question

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

k2 + 10k +

Answer 1

To complete the square for the polynomial \( k^2 + 10k \), we can follow these steps:

1. Start with the term \( k^2 + 10k \).
2. Take the coefficient of \( k \), which is \( 10 \), divide it by \( 2 \), and square the result:

\[
\left(\frac{10}{2}\right)^2 = 5^2 = 25
\]

3. Add and subtract this square inside the expression:

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

This rearranges to:

\[
(k + 5)^2 - 25
\]

Thus, the number that makes the polynomial a perfect-square quadratic is \( 25 \).

So the completed expression is \( k^2 + 10k + 25 \).