Need help with complex conjugates theorem and Descartes' rules of signs?

Question

Hi, can someone please explain how to do these Conjugates theorem and Decartes' Rules of Signs problems because I am soo confused.

Here is one Decartes' problem
1.) f(x) = x^10 - x^8 + x^6 - x^4 + x^2 -1

Here is a Complex Conjugates problem
2.)f(x) = x^3 - 4x^2 + 6x - 4; 2

Answer 1

The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or less than it by a multiple of 2. Multiple roots of the same value are counted separately.

1.) f(x) = x^10 - x^8 + x^6 - x^4 + x^2 -1
Applying the rule, there must be 1, 3, or 5 positive roots.
Grouping,
(x^10 - x^8) + (x^6 - x^4) + (x^2 -1) =
x^8(x^2 - 1) + x^4(x^2 - 1) + (x^2 -1) =
(x^2 - 1)(x^8 + x^4 + 1) =
(x + 1)(x - 1)(x^8 + x^4 + 1) has
one positive, one negative, and eight complex roots.

2)
f(x) = x^3 - 4x^2 + 6x - 4 = ; 2
(1/x) (x^4 - 4x^3 + 6x^2 - 4x + 1 - 1) =
(1/x) ((x - 1)^4 - 1) =
(1/x) ((x - 1)^2 - 1)((x - 1)^2 + 1) =
(1/x) ( (x - 1) - 1)(x - 1) + 1) ((x - 1) + j1) ((x - 1) - j1)=
(1/x) ( (x - 2)(x)(x - 1 + j1)(x - 1 - j1) =
(x - 2)(x - 1 + j1)(x - 1 - j1)