Question

how to factorise x^5+1​

Answer 1

Answer:

$\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)$

Step-by-step explanation:

$x^5+1$

We can write 1 as $1^5$

$x^5+1^5$

use identity: $\:x^n+y^n=\left(x+y\right)\left(x^{n-1}-x^{n-2}y+\dots -xy^{n-2}+y^{n-1}\right)$

$\left(x+1\right)\left(x^4-x^3+x^2-x+1\right)$

Answer 2

The zero of the polynomial is −1.
So divide the equation by (x+1)
By dividing the equation, we get
(1+x
5
) =(x+1)(x
4
−x
3
+x
2
−x+