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

Question

k2 − 28k +

Answer 1

To complete the square for the polynomial $k^2-28k$, we follow these steps:

1. Take the coefficient of the $k$ term, which is $-28$.
2. Divide it by $2$:
   $$\frac{-28}{2}=-14$$
3. Square the result:
   $$(-14{)}^2=196$$

Now, we add this square to the polynomial to complete the square:

$$k^2-28k+196$$

Thus, the number that you need to fill in to make the polynomial a perfect-square quadratic is $\boxed{{\displaystyle 196}}$.

The completed square expression is:

$$(k-14{)}^2$$