To determine the value that must be added to the expression x² + 16x in order to make it a perfect square trinomial, we can follow a systematic process.
A perfect square trinomial takes the form of (a + b)², which expands to a² + 2ab + b². In our case, we have the quadratic term x² and the linear term 16x. The first step is to identify the coefficient of the x term, which is 16.
Next, we divide the coefficient of the x term by 2:
- Coefficient of x: 16
- Divide by 2: 16 / 2 = 8
Then, we square the result of this division:
- Square of 8: 8² = 64
Thus, the value that needs to be added to the expression x² + 16x to make it a perfect square trinomial is 64.
After adding 64, the expression will be:
- x² + 16x + 64
This can be factored as (x + 8)², confirming that it is indeed a perfect square trinomial. Therefore, the answer is:
- 64