Which of the following is the reciprocal of x2 – 2x – 8?

Question

anonymous · Answer

A. (x + 2)(x – 4) 	
	B.                 1             
                 (x + 2)(x – 4) 	
	C.            1     
                 (x – 8) 	
	D.            1     
                 (x + 2)

anonymous · Answer

Well, What does a reciprocal mean?

anonymous · Answer

What would the reciprocal of say 10 be?

anonymous · Answer

0.1

anonymous · Answer

Right. So when you foil $\ \huge \color{blue} x^2-2x-8 $, what do you get?

anonymous · Answer

Reciprocal is 1/x.
$$\frac{1}{x^2-2x-8}$$
Factoring that out;
$$\frac{1}{(x-4)(x+2)}$$
Therefore B

anonymous · Answer

$\ \huge (x+2)(x-4) $. You can also write that as a reciprical: $\ \huge \frac{1}{(x+2)(x-4)} $. So, the correct answer is B. Do you understand that?