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

Question

h2 − 26h +

Answer 1

To complete the square for the polynomial $h^2-26h$, we need to find a number that makes it a perfect-square quadratic.

1. Take the coefficient of $h$, which is $-26$.
2. Divide this number by 2: $$-26÷2=-13$$
3. Square the result: $$(-13{)}^2=169$$

Therefore, we fill in the blank with 169.

Putting this all together, the expression $h^2-26h+169$ can be rewritten as: $$(h-13{)}^2$$

Thus, the number that makes the polynomial a perfect-square quadratic is 169.