To find the factors, it's basically trial and error.
You should use the factor theorem, where if you a have a function:f(x), then if (x-p) is a factor of f(x), f(p) will be equal to zero.
In your example, trying (x-1) gives:
f(1) = 2 - 3 - 1 + 1 = -1
So, (x-1) is not a factor. Let's try (x+1). [You normally try out the factors of the coefficient of the highest power of x and the term with the smallest power of x]
f(-1) = -2 -3 + 1 + 1 = -3
So, (x+1) is not a factor.
Let's try (x-2)
f(2) = 16 - 12 - 2 + 1 = 3
(x-2) is not a factor. Let's try (x+2)
f(-2) = -16 - 3 + 2 + 1 = -16
(x+2) is not a factor either...
Well, now, let's take (x - 0.5).
f(0.5) = 0.25 - 0.75 - 0.5+1 = 0
So, we get (x - 0.5) as a factor.
(2x - 1) as a factor.
Do you know how to use long division to continue the factoring?