Question

Need help simplifying an equation. It will be in the reply section. Will fan and Medal!

Answer 1

\[\frac{ k(6k^2 - 3k - 1) + 18 k^2 +12k +2 }{ 2 }\]

Answer 2

@SolomonZelman @sweetburger

Answer 3

@ganeshie8

Answer 4

Well distribute the k over the (6k^2-3k-1)
then group the like terms
then start factoring and see what you get and you might have to then do some long division, just try this out yourself and see where you get.

Answer 5

ok. One sec

Answer 6

stuck at \[\frac{ 6k^3 + 15k^2 + 11k +2 }{ 2 }\] @iambatman

Answer 7

Ok nice you did the first two steps, I think the "rational root theorem" is a good way to simplify more https://www.youtube.com/watch?v=XrmpPMKQRmE here is a vid on how to do it, you basically need to find the roots of k

Answer 8

Since k has so many roots

Answer 9

ok.

Answer 10

Im at school and it won't let me access that video. Do you have another way of explaining it?

Answer 11

Well basically we'll have many roots, I don't know how many haha, like \[k = \pm \frac{ 1 }{ 2 }, k = \pm \frac{ 1 }{ 3 }\] etc we call this linear factors of k and for all of them we can safely assume it will be (k+1) so it should look sort of like \[\frac{ (k+1)((6k^3+15k^2+11k+2) }{ (k+1) }\] (I did not add the 2 in the numerator, we can add that later at the end).
With this you can do long division since you have (k+1) it gives us something to divide by

Answer 12

So once you do the long division process (6k^3+15k^2+11k+2)/(k+1) etc... you should get \[\frac{ (k+1)(6k^2+9k+2) }{ 2 }\]

Answer 13

Ok that's easy enough!

Answer 14

Uhg OS keeps messing up for me, I was saying you can probably leave it as when you collected like terms depending how harsh your teacher is haha, so you can simplify term by term to, after you collect like terms getting, which you can see is much easier.
\[3k^3+\frac{ 15k^2 }{ 2 }+\frac{ 11k }{ 2 }+1\]

Answer 15

She wanted it the way we have it after the Rational root theorem

Answer 16

This was part of a mathematical Induction problem and I don't know if our final equation proves it correct or not. Do you know anything about mathematical induction? @iambatman

Answer 17

Yes, I know about induction but I think you will get the same answer...

Answer 18

The original equation was http://learn.flvs.net/webdav/educator_precalc_v12/module07/imagmod7/07_04_01c_02.gif

Answer 19

I cannot see it, as I don't have an account, maybe you can take a screenshot.

Answer 20

(n(6n^2-3n-1))/2

Answer 21

@iambatman