Question

Factor the given expression.

x2 + 16
+ 64
O A. (x+4)2
B. (x + 16)(x + 4)
c. (x+3)(x - 8)
OD. (x+8)2

Answer 1

D. (x+8)^2

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.