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

Question

q2 − 4q +

Answer 1

To complete the square for the quadratic \( q^2 - 4q \), we follow these steps:

1. Take the coefficient of \( q \), which is \(-4\).
2. Divide it by 2: \(-4 \div 2 = -2\).
3. Square the result: \((-2)^2 = 4\).

Now, we add this squared value to the polynomial:

\[ q^2 - 4q + 4 \]

This expression can be factored as:

\[ (q - 2)^2 \]

Therefore, the number that makes the polynomial \( q^2 - 4q \) a perfect-square quadratic is 4.