Question

Please help!

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

A. (x + 2)(x – 4)

B. 1/(x + 2)(x – 4)

C. 1/(x – 8)

D.1/(x + 2)

A, B, C, or D? Please explain (:

Answer 1

A reciprocal is just 1 divided by the original number. So in this case it's 1/(x^2 - 2x -8). Since that's not one of the answers, looking at your choices suggests that you have to factor. So you have:

(x )(x )

8 could be 4 x 2 or 2 x 2 but only 4 x 2 is going to give you the 2 for the 2x:

(x 2)(x 4)

Now you just have to figure out the signs. You want a -2x, so that tells you you want a -4 and +2:

(x + 2)(x - 4)

Now check the answers again.

Answer 2

Oops, I should have clarified that (x + 2)(x - 4) is still under the 1 for the reciprocal:

\[\frac{1}{(x + 2)(x - 4)}\]

Answer 3

Ah so it's B?

Answer 4

Yep.

Answer 5

Thank you (:

Answer 6

Any time!