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avatar+1016 

One of the zeros of the polynomial function is 2.
 

 

 Feb 8, 2018

Best Answer 

 #2
avatar+8780 
+3

Use synthetic division to find  (x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2) .

 

 

(x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2)   =  x3 - x2 - 25x + 25

 

So

 

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x3 - x2 - 25x + 25)

 

Now we can factor   x3 - x2 - 25x + 25  .

 

x3 - x2 - 25x + 25   =   x2(x - 1) - 25(x - 1)   =   (x - 1)(x2 - 25)   =   (x - 1)(x - 5)(x + 5)

 

So

 

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x - 1)(x - 5)(x + 5)

 Feb 8, 2018
edited by hectictar  Feb 10, 2018
 #2
avatar+8780 
+3
Best Answer

Use synthetic division to find  (x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2) .

 

 

(x4 - 3x3 - 23x2 + 75x - 50)  /  (x - 2)   =  x3 - x2 - 25x + 25

 

So

 

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x3 - x2 - 25x + 25)

 

Now we can factor   x3 - x2 - 25x + 25  .

 

x3 - x2 - 25x + 25   =   x2(x - 1) - 25(x - 1)   =   (x - 1)(x2 - 25)   =   (x - 1)(x - 5)(x + 5)

 

So

 

x4 - 3x3 - 23x2 + 75x - 50   =   (x - 2)(x - 1)(x - 5)(x + 5)

hectictar Feb 8, 2018
edited by hectictar  Feb 10, 2018

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