Factorise the following:

Question

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

The answer is x(x+1)(x-1)^2
but I cannot understand how to get this answer. Can someone please show me the working? Thanks!

Answer 1

factor out x
x(x^3-x^2 -x + 1)
Now, on the cubic part, notice the 1 a the end. That means the factors have to multiply to one.
x( x(x^2-1) -(x^2-1))
x(x-1)(x^2-1) and you can factor the x^2-1 into two factors..