By regrouping the terms, a factor emerges:
4+4x³-(x²+x⁵)=4(1+x³)-x²(1+x³)=(4-x²)(1+x³).
Both 4-x² and 1+x³ factorise further.
4-x²=(2-x)(2+x).
1+x³ clearly has a zero when 1+x³=0, x³=-1 so x=-1 meaning 1+x is a factor. By dividing by this factor we get 1-x+x². Now we have all the factors: (1+x)(1-x+x²)(x-2)(x+2).