Question

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

Answer 1

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

Answer 2

Well, What does a reciprocal mean?

Answer 3

What would the reciprocal of say 10 be?

Answer 4

0.1

Answer 5

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

Answer 6

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

Answer 7

\(\ \huge (x+2)(x-4) \). 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?