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

Question

k2 − 16k +

Answer 1

To complete the square for the polynomial \( k^2 - 16k \), we first need to determine the term that will make it a perfect-square quadratic.

1. Take the coefficient of \( k \), which is \(-16\).
2. Divide it by 2: \(-16 / 2 = -8\).
3. Square this result: \((-8)^2 = 64\).

Now, we add \( 64 \) to the polynomial:

\[ k^2 - 16k + 64 \]

Thus, the number that makes the polynomial a perfect-square quadratic is \( \boxed{64} \).

Now, we can rewrite the expression as a perfect square:

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