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

k2 + 16k + 

To complete the square, we follow these steps:

Given the quadratic expression:  
\[ k^2 + 16k \]

1. **Take half of the coefficient of \(k\)**:  
   The coefficient of \(k\) is 16, so half of it is:
   \[
   \frac{16}{2} = 8
   \]

2. **Square that value**:
   \[
   8^2 = 64
   \]

3. **Add this value to the expression** to complete the square:
   \[
   k^2 + 16k + 64
   \]

Now the expression \(k^2 + 16k + 64\) is a perfect square, which can be factored as:
\[
(k + 8)^2
\]

The number that completes the square is **64**.

Would you like to see more details or ask questions?  
Here are some related questions for further practice:

1. Complete the square for \(x^2 + 10x + \_\_\_\_\).
2. Factor the quadratic \(y^2 + 12y + 36\).
3. Solve \(k^2 + 16k + 64 = 0\) using the square completion method.
4. Expand \((k + 8)^2\) and verify that it matches the original expression.
5. How does completing the square help in solving quadratic equations?

**Tip**: Completing the square is a powerful method to convert a quadratic into vertex form, which makes it easier to find the maximum or minimum value of a quadratic function.

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
k^2 + 16k +

Learn how to complete the square for the expression k^2 + 16k by following a step-by-step process. This example illustrates the concept of completing the square and the quadratic expression factorization method, which is essential for students in Grades 8-10.

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