What is the Simplified Expression for 6n^5+15n^4+10n^3-n?

[rover]

Hi,
Could someone help me to simplify this expression:

6n^5+15n^4+10n^3-n

Thanks,

 

[TD]

You can start by factoring out n

 

[rover]

I forgot to mention that it should be in the form of:
n(n+1)(...

thanks

 

[TD]

Well, n is a common factor so can you start yourself?
After that, it'll be a bit harder to find factors but still doable (by finding zeroes of the polynomial!).

Try factoring out n yourself ?

 

[rover]

thanks for the fast reply!

I have tried to get the roots (the zeros). After taking n as a common factor we have:
n(6n^4+15n^3+10n^2-1)

" 6n^4+15n^3+10n^2-1" has 4 roots and two of them are "strange" (dont know a better word). what i mean by strange is that one is unable to write them as 1/2, 1/3 or x/y.

the value of the root is: -1.263763...
the other root is: 0,263763...

does anyone know how to deal with these kind of problems

 

[TD]

If a is a zero, then you can factor out (x-a)
Try adding up all coëfficiënts of the even powers in x and the ones of the odd powers in x, if these 2 are the same then -1 is a zero and thus, (x+1) a factor.

 

[rover]

Thanks TD for your very fast replies

By taking the roots i get the simplification:

(x+1.263763...)(x+1)(2x+1)(x-0,263763...)

I did not understand what u mean (i have the same powers for all x (=1), or?)
However, can i by any method cancel the 0.263763...

 

[Hurkyl]

I forgot to mention that it should be in the form of:
n(n+1)(...

Then, you should be able to divide your original polynomial by n(n+1) and see what's left.

By the way, "strange" is irrational.

 

[rover]

I solved it!

if you multiply those irrational numbers you get a rational value!
The simplified answer is

x(x+1)(2x+1)(3x^2+3x-1)