Question

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

h2 − 10h +

Answer 1

To complete the square for the polynomial \( h^2 - 10h + \_\_ \), we need to find a number to add that will make the expression a perfect square.

The general formula for completing the square for a quadratic expression in the form \( h^2 + bh \) is to take half of the coefficient \( b \) of \( h \), square it, and add it to the expression.

In your case, the coefficient \( b \) is \(-10\).

1. Take half of \(-10\):
\[
\frac{-10}{2} = -5
\]

2. Square it:
\[
(-5)^2 = 25
\]

So, the number that makes the polynomial a perfect-square quadratic is \( 25 \).

Thus, the completed expression is:

\[
h^2 - 10h + 25
\]

This can be factored as:

\[
(h - 5)^2
\]

So, the number you fill in is **25**.