Question

x^3-5x^2-x+5 factorise it

Answer 1

hello users ......
we have given equation is 
 = x³ - 5x² - x +5 = 0  .........(1)

solution :-

suppose x = -1 is the solution of the given equation 

let's  check ,put x = -1 in equ.   (1)
=>  (-1)³ - 5(-1)² -(-1) +5 = 0
=> -1 -5 +1 +5 =0 
=> 0 = 0

so x= -1 is the solution 
and (x+1) is the factor of equation 

let's divide 
 ( x³ - 5x² - x +5)  by (x+1) 

we get 
  x+1 I  x³ - 5x² - x +5 I x² - 6x + 5
            x³ +x² 
         ------------  
                -6 x² -x +5 
                -6 x² -6x 
                ----------------
                         5x + 5
                         5x + 5
                        -----------
                           zero 
                        -----------

=>  x³ - 5x² - x +5 = (x+1) ( x² -6x +5) 
= (x + 1) ( x² -5x - x + 5 ) 
= (x +1) { x(x -5) -1( x - 5) } 
= (x+1) (x - 5) (x-1) = 0 

hence 
x = -1, 5 , 1 answer 

✪✪ hope it helps ✪✪