Question

x^9-x^6-x^3+1

Answer 1

Please help.

Answer 2

Do you want the roots or derivative or something else?

Answer 3

\[x^9-x^6-x^3+1\]

Answer 4

or do u want to factorize ?

Answer 5

Factor.

Answer 6

right, can u take out something common from first 2 terms ?

Answer 7

x^2?

Answer 8

is x^6 common ?
from x^9-x^6

Answer 9

(X^3-1)(X^6-1)

Answer 10

\[\large{1} = x^0 \]You might want to note the above by the way.

Answer 11

Then factorise each term further by using the cube roots eg. (x-1)(X^2+x+1) for(x^3-1) and (x^2-1)(x^4+x^2+1) for (x^6-1) and then (x+1)(x-1) for (x^2-1)

Answer 12

(x-1)(x-1)(x+1)(x^2+x+1)(x^4+x^2+1) You can test by expanding

Answer 13

if the sum all coefficients/constants of term equal zero :
1-1-1+1 = 0
then one of factor that polynom is (x-1), and next we can find other factors by using syntetic's method

Answer 14

Another way to proceed is to set x^3 = t ->

t^3 -t^2 -t +1 and you see that plus/minus 1 are roots straight away..