How to factorize polynomials to the 5th degree? I have the polynomial:
$$2x^5-x^4+10x^3-5x^2+8x-4$$
and I know that the final result is:
$$(2x-1)(x^4+5x^2+4) = (2x-1)(x^2+1)(x^2+4)$$
But how would you do it step by step? I've seen a couple of videos and blogs about it, but they mostly use examples, where their is a common factor between the expressions but in this case their are none.

The question slightly wrong in my opinion. Please try multiplying the factors or the eqn. and lets see if you will get back the original question.
The correct equation is $P(x): 2x^5-x^4-10x^3+5x^2+8x-4$
Group and Factorize: $(2x^5-x^4) (-10x^3+5x^2) (8x-4) =0$
                 $x^4(2x-1)   -5x^2(2x-1)  4(2x-1)$

        Factor out $(2x-1)$ then we have $x^4-5x^2+4$

Our first factor of the equation is $(2x-1)$
This looks like a quadratic form but our first coefficient has 4th degree
look let's expand $x^4-5x^2+4$ and we have $(x^2-4)$ and $(x^2-1)$. $-4$ and $-1$ when added will be $-4-1 = -5$ and when multiply $-4x-1 = 4. x^2 x x^2 = x^4$
so its just splitting them and distributing them on $-4$ and $-1$ which are the product of the constant and sum of the middle term.
Now with $(x^2-4)$ and $(x^2-1)$ we can have $(x-2) (x+2)$ and $(x-1) (x+1)$.
so our final factors of the polynomial are $(2x-1) (x-2) (x+2) (x-1) (x+1)$
Therefore; the zeros of the polynomial are $1/2, 2, -2, 1, -1$.
