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

In summary, the conversation is about simplifying a polynomial expression by factoring out a common factor and finding its roots. The roots are irrational numbers, but the simplified answer can be written as a rational expression in terms of those roots.
  • #1
rover
Hi,
Could someone help me to simplify this expression:

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

Thanks,

:smile:
 
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  • #2
You can start by factoring out n :smile:
 
  • #3
I forgot to mention that it should be in the form of:
n(n+1)(...

thanks
 
  • #4
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 ?
 
  • #5
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
 
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  • #6
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.
 
  • #7
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...
 
  • #8
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.
 
  • #9
I solved it! :smile: :smile: :rolleyes:

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

x(x+1)(2x+1)(3x^2+3x-1)
 

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

What does it mean to simplify an expression?

Simplifying an expression means to reduce it to its most basic form by combining like terms, removing parentheses, and applying mathematical operations according to the order of operations.

How do I simplify an expression?

To simplify an expression, start by combining like terms (terms with the same variables and exponents). Then, remove any parentheses by distributing any coefficients outside of them. Finally, apply any remaining mathematical operations according to the order of operations.

Why is it important to simplify an expression?

Simplifying an expression makes it easier to work with and understand. It also allows for a quicker and more accurate solution to the problem at hand.

Can I use different methods to simplify an expression?

Yes, there are multiple methods that can be used to simplify an expression, such as the distributive property, combining like terms, and applying the order of operations. The method used may vary depending on the specific expression.

Are there any common mistakes to avoid when simplifying an expression?

Some common mistakes to avoid when simplifying an expression include forgetting to distribute coefficients, incorrectly applying the order of operations, and combining unlike terms. It is important to double check your work and carefully follow each step in the simplification process.

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