Answer: The correct option is (A). 64.
Step-by-step explanation: We are given to find the value of c that makes the following polynomial a perfect square.
[tex]P=x^2+16x+c.[/tex]
We will be using the method of completing the square to find the value of c.
We have
[tex]P\\\\=x^2+16x+c\\\\=x^2+2\times x\times 8+c\\\\=(x^2+2\times x\times 8+8^2)+c-8^2\\\\=(x+8)^2+c-64.[/tex]
Therefore, to make the polynomial P a perfect square, we must have
[tex]c-64=0\\\\\Rightarrow c=64.[/tex]
Thus, the required value of c is 64.
Option (A) is CORRECT.
