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

Question

t2 − 4t +

Answer 1

To complete the square for the quadratic expression \( t^2 - 4t + __ \), we need to find a number to add that will make it a perfect square.

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

Now we can complete the square:

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

This expression can be rewritten as:

\[ (t - 2)^2 \]

So, the number that you need to fill in is \( 4 \). Thus, the completed expression is:

\[ t^2 - 4t + 4 = (t - 2)^2 \]