simplify ½n^4 - n^3 + n^2 + 4½n?

Question

(^ = to the power of)

Can this simplifyed any further, probably by factoriseing, and could you show me the method.

Thank you

Answer 1

yes this can be facotored

1st remove denominator
(n^4-2n^3+2n^2-9n)/2
n is in all terms
= n(n^3-2n^2+2n -9)/2
if cubic has rational roots it is factor of -9 that is 1/-1/3/-3/9/-9

it does not have rational factors
so cannot be factored further and we stop at
n(n^3-2n^2+2n -9)/2

Answer 2

Let's multiply this by 2 just so it looks easier.

n^4 - 2n^3 + 2n^2 + 9n

Let's take out n:

n(n^3 -2n^2 + 2n + 9)

Factor:

n[(n ? 1)(n ? 3)(n ? 3)]

The coefficient of n^2 would have to be some combination of 3, 3, and 1, with appropriate signs. You can't make 2 out of 3, 3, and 1 no matter how you slice it.

The coefficient of the n term would have to be some combination of 9, 3, and 3, with appropriate signs. You can't make 2 out of 9, 3, and 3 no matter what.

This cannot be factored any more.

Answer 3

the simplist solution is

(1/2)n(n^3-2n^2+2n+9)

the best way to find a factor is the
remainder theory

f(1)=1/2-1+1+41/2 is not equal to 0
hence,n-1 is not a factor

if f(a)=0, n-a is a factor
if f(-a)=0, n+a is a factor and so on
i hope that this helps

Answer 4

n / 2 is the only simple factor.

= (n / 2)(n^3 - 2n^2 + 2n + 9)

Answer 5

if the N was 2 then the sum would be
1 - 8 + 4 + 9
thats all i can think of

Answer 6

taking lcm
1/2(n^4-2n^3+2n^2+4n)
1/2n(n^3-2n^2+2n+4)
it has no further factors