Question

simplify x-7/x^3-127

Answer 1

I'm trying to factor x^3-127...but am not sure if that is the right way to solve it

Answer 2

that's your question right

Answer 3

yes

Answer 4

\(x^3\) is a cube. what about \(127\)?

Answer 5

just 127

Answer 6

If \(127=b^3, a^3=x^3\), then you have a difference of cubes:
\[(a^3-b^3) = (a-b)(a^2+ab+b^2)\]However, 127 isn't a perfect cube.

Answer 7

\[x^3-125 = (x-5)(x^2+5x+25)\]

But that's not our problem. \[x^3-127\]is irreducible. Can't be factored.

Answer 8

oops 125

Answer 9

sorry

Answer 10

Well, I just happen to have a writeup of that problem here somewhere…now where did I leave that? :-)

Answer 11

Its here...I think I just saw it

Answer 12

(x-5)(x^2+5x+25)

Answer 13

We can test it out. Let x = 6, for example:
\[(6)^3 - 125 = 216-125 = 91\]\[(6-5)(6^2+5(6)+25) = 1(36+30+25) = 91\checkmark
\]

Answer 14

so what will happen to x-7