Answer:
D. (x+8)^2
Step-by-step explanation:
x^2 + 16x + 64
We are factoring a quadratic trinomial in which the first term is x^2.
We need to find two numbers whose product is 64 and whose sum is 8.
8 * 8 = 64
8 + 8 = 16
The numbers are 8 and 8.
x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2
Check: If (x + 8)^2 is indeed the correct factorization of x^2 + 16x + 64, then if you multiply out (x + 8)^2, you must get x^2 + 16x + 64.
(x + 8)^2 =
= (x + 8)(x + 8)
= x^2 + 8x + 64
= x^2 + 16x + 64
We get the correct product, so our factorization is correct.
