Factorization

16x^5 - 20x^3 + 5x + 1= (x + 1) (16x^4 - 16x^3 - 4x^2 + 4x + 1)= (x + 1) (16x^4 - 16x^3 + 4x^2 - 8x^2 + 4x + 1)= (x + 1) (16x^4 - 16x^3 + 4x^2 - (8x^2 - 4x) + 1)= (x + 1) [(4x^2 - 2x)^2 - 2(4x^2 - 2x) + 1]= (x + 1) (4x^2 - 2x - 1)^2When (x + 1) (4x^2 - 2x - 1)^2 = 0 ,x + 1 = 0 or 4x^2 - 2x - 1 = 0 ,x = - 1 or x = (1 ± √5)/4 (double roots)