#### Answer

C: $(x+2)(x-8)$

#### Work Step by Step

We can test each case to determine which is the factored form of $x^2-6x-16$, as this is a multiple choice question:
A: $(x+2)(x+8)=x^2+2x+8x+16=x^2+10x+16$
B: $(x-2)(x+8)=x^2-2x+8x-16=x^2+6x-16$
C: $(x+2)(x-8)=x^2+2x-8x-16=x^2-6x-16$
D: $(x-2)(x-8)=x^2-2x-8x+16=x^2-10x+16$
From this, we see that C is the correct answer.