Factor the expression 5x^3 - x^2 + 5x - 1

Hello,

5x^3-x^3+5x-1=x²(5x-1)+(5x-1)=(5x-1)(x²+1)=(5x-1)(x-i)(x+i)

Group like terms


Find the common factor of each term and simplify



Additional :-
Find the roots of each of the terms:
(i) 
      - using the quadratic equation ()
      -       OR      
      - Since the discriminant is negative () [a negative number cannot be rooted] then this equation has no real roots (imaginary roots)

(ii) 
         - Simply Solve for x
              5x - 1 = 0
                    5x = 1
                      x = 

Thus the only solution this has or the only root this expression has is    OR  0.2