Question

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

f2 + 16f +

Answer 1

To complete the square for the polynomial \( f^2 + 16f \), we first need to identify the coefficient of the \( f \) term.

1. The coefficient of \( f \) is 16.
2. To complete the square, we take half of this coefficient, which is \( \frac{16}{2} = 8 \).
3. Next, we square this value: \( 8^2 = 64 \).

Now, we can add and subtract this value (64) to complete the square:

\[
f^2 + 16f = (f^2 + 16f + 64 - 64) = (f + 8)^2 - 64
\]

Thus, the value to fill in the blank to make the polynomial a perfect square is \( 64 \).

So the completed polynomial is:
\[
f^2 + 16f + 64.
\]