How do you factorise this? i know the factorised form but i just don't know how you arrive there.

x^4 + x^3 + 2x - 4

ok i know the answer is (x-1)(x+2)(x^2+2) but i just dont get how you arrive at that, please help me out with some step by step instructions. thanks!

look at the factors and powers
1 even
1 odd
2 odd
-4 even
so 1 is a root
-2 is also a root
so you can get (x-1)(x+2)
then do a long division you can get (x^2+2) which can't be factored

If you know that x = 1 is a zero, then the quotient is x^3 + 2x^2 + 2x + 4, using Synthetic Division.

Using Synthetic Division again with x = -2 as a zero, the quotient now is x^2 + 1, which does not factor using real numbers.

So the factorization of the polynomial is (x - 1)(x + 2)(x^2 + 2).