Question 61715
F(x)  = x^3 - 4x^2 + 13 x + 50         ---->(1)
Check the last number, which is 50
Now find the factors of 50, 
That is 50 ---- 1 , 2 , 5 ,25
So take all the numbers ---- 1 , -1 ,2 ,-2 ,5,-5,25 , -25
Now take the first factor 1. put in equation(1), we get
F(1) = 1^3 - 4*1^2 + 13*1+ 50 = 48
F(1) is not  equal to zero.
Like this find for different numbers,
Then we find that F(-2) is equal to zero.
So x = -2 is a zero.  ------>(2)
Now rewrite the above equation we find that...
 x+2 = 0
 Now take this and divide equation (1), 
                   x^2 - 6x + 25
                 ---------------------------
(x+2)            | x^3 - 4x^2 + 13 x + 50                       Subtract, we 
get         
                 | x^3 + 2x^2        
                 |        - 6x^2 +13x
                 |        - 6x^2 - 12x                                 Subtract , we get     
                 |                     25x + 50
                                       25x + 50                          Subtract,  we get
                                         0                            

We  get  x^2 - 6x + 25 
Simplify this quadratic equation, we get
x =  - (-6) +-  sqrt(6^2 - 4* 1* 25
                    2
x = 3 + 4i  and x = 3 - 4i

Therefore the zeroes are x = 2 and  x = 3 + 4i , x = 3 - 4i