+0  
 
+1
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2
avatar+660 

Factor the polynomial function over the complex numbers.

AngelRay  Feb 8, 2018
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 #2
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+1

I'm not sure what you're taught.....but....I see that 2 is a root....so....we can use synthetic division to find the other roots

 

 

2  [    1      -1     0     -2      -4  ]

                   2    2      4       4

     ___________________

         1      1      2      2      0

 

Our remaining polynomial is  

 

x^3  + x^2  + 2x  +  2

 

And -1 is a root...so...performing synthetic division  again, we have

 

 

-1  [  1     1        2      2   ]

              -1        0     -2

      _________________

        1     0        2      0

 

 

The remaining polynomial is  

 

x^2  +  2.....  setting this to 0 to find the other roots, we have

 

x^2  +  2  = 0

 

x^2  = -2       take both roots

 

x = ±  √2  i

 

 

So.....the factorization is :

 

f(x)   =  (x - 2) (x + 1) (x -   √2 i )  ( x +   √2 i  )

 

 

 

cool cool cool

CPhill  Feb 8, 2018

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