Final answer:
To make the polynomial x^2 + 26x + ? a perfect square trinomial, the missing value is 169.
Step-by-step explanation:
To make the polynomial x^2 + 26x + ? a perfect square trinomial, we need to find the missing value. Since the first term is x^2, we know that the square root of the first term will be the first term of our perfect square trinomial. In this case, it will be x.
Next, we take the square root of the third term, which will be the last term of our perfect square trinomial. Since the third term is missing, we need to find its value by taking half of the second term and squaring it. In this case, half of 26 is 13, and 13 squared is 169. So the missing term is 169.
Therefore, the value in place of the question mark to make the polynomial a perfect square trinomial is 169.