X 5 1
Did you factor in x 51? 3
x 51 =?
updateExplain the steps ... I don't care about the answer.
If x 5 1 = 0, then the root of x = 1
There (x1) is an element.
Use the division to divide x 5 1 by (x1)
> (x1) (x 4 + x 3 + x 2 + x + 1)
(x 1) * (x 4 + x 3 + x 2 + x + 1)
Do you know the geometric series? In general, x n1 can be factored:
(x 1) * (1 + x + x 2 + x 3 + .... + x (n 1))
Are you referring to the geometric series? Suppose we have a series whose value is S. add.
S = 1 + x + x 2 + x 3 + x 4 + x 5 + ... + x (n 1)
Multiply both sides by x.
S * x = x + x 2 + x 3 + ... + x (n 1) + x n
Subtract the first equation from the second equation.
Sx S = x n 1
S * (x 1) = (x n1)
Remember S = 1 + x + x 2 + x 3 + ... + x (n 1)
NS
(x 1) * (1 + x + x 2 + x 3 + ... + x (n 1)) = x n 1
x 51
= (x1) (x 4 + x 3 + x 2 + 1)
X 5 1
X 5 1
(x1) (x 4 + x 3 + x 2 + x + 1)
Factor X51
