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

Question

t2 + 12t +

Answer 1

To complete the square for the polynomial \(t^2 + 12t\), we need to find a number to add that will make it a perfect-square quadratic.

1. Start with the coefficient of \(t\), which is 12.
2. Take half of this coefficient, which is \( \frac{12}{2} = 6 \).
3. Square this result: \(6^2 = 36\).

Now, we can express the original polynomial:

\[ t^2 + 12t + 36 \]

This can then be factored as:

\[ (t + 6)^2 \]

Thus, the number you need to add to make the polynomial a perfect-square quadratic is \(36\).