x8+x4+1
12x+1
There are clearly no real solutions, but you can factor it into
(x^2-x+1)(x^2+x+1)(x^4-x^2+1) = 0
because
x^8+x^4+1 = x^8+2x^4+1 - x^4
= (x^4+1)^2 - (x^2)^2
a difference of two squares
Now you can find the roots of those quadratics
The given expression is x^8 + x^4 + 1. This is a polynomial expression in the variable x.
To simplify this expression, there isn't much we can do other than combining like terms by adding the coefficients of the same power of x. In this case, each term has a different power of x, so we cannot combine any terms. Therefore, the expression x^8 + x^4 + 1 is already in its simplest form.
If you were looking for a specific value of this expression, you would need to substitute a value for x. For example, if you wanted to evaluate the expression when x = 2, you would substitute x = 2 into the expression:
(2^8) + (2^4) + 1 = 256 + 16 + 1 = 273
So, when x = 2, the expression x^8 + x^4 + 1 evaluates to 273.