It is easy to see that expression =0 when x=1 It follows that x-1 is a factor. The 2nd bracket then must begin with 2x^2 and end in -1

SO 2x^3-3x+1= (x-1)(2x^2 _1) Multiplying these out as they are would give a term -2x^2 which we dont want. Putting =2x in the middle of the 2nd bracket will get rid of this. So 2x^3-3x+1=(x-1)(2x^2+2x-1) Notice this also gives us the required -3x term.