The equation 3x^3 + 5x^2 = 3x + 5 has got 3 roots and hence the factors of the left hand side of the equation 3x^3 + 5x^2 - 3x - 5 = 0 are

• Easiest way :-
  to find the factor of the equation 3x^3 + 5x^2 - 3x - 5 = 0 is that this equation is just the re positioned form of the equation 3x^3 + 5x^2 = 3x + 5 so just find the factor of this equation .
  in order to get that u need to see this equation as an equation that is already served in the form of split ted middle term so u will get by taking common the value of x as (-5/3 , -1 ,1 ) ... which are the factors for the latter equation .
  
  lengthy way :-
  (quite lengthy) take the second equation in the question and apply the factor finding procedure for cubic equation that is pick up the last constant and find its factors , so here it is 5 , -5 , 1 , -1 . after this neglect -5 and 5 coz by replacing x by 5 and -5 we get a bigger constant and we need it to be equals to zero . so we are getting zero with 1 and -1 now so x = 1 and x= -1 rearranging these we get x-1=0 and x+1 = 0 , now divide the cubic equation provided by the division of an equation method and each time u would be left with a questiont of a quadratic equation . after this find the roots of these two quadratic equation by split the middle term and u will get answer as -5/3 , -1 ,+1... same as the easier way .
• 7 years agoHelpfull: Yes(0) No(0)