Hi,

(x-2)(x+6i) 

 (x^2 -2x +6i - 12i) = (x^2 -2x - 6i)

 (x^2 -2x -6i)(x-6i)  to finish Up

 x^3 - 2x^2 - 6ix  - 6ix^2 +12ix - 36   

combine Like terms

x^3 -2(1+3i)x^2 +6ix - 36

 

Answer by LinnW(1048)   (Show Source): You can put this solution on YOUR website!
 To be a polynomial we need real coefficients

so we want something like:

(x-2)(x+6i)(x-6i)

This expands to 

(x-2)( x^2 - (6i)^2 )

(x-2)( x^2 - ( 36i^2 ) )

(x-2)( x^2 - ( 36(-1)) )

(x-2)( x^2 + 36 ) expanded gives us

x^3 -2x^2 +36x -72

So our polynomial could be

x^3 -2x^2 +36x -72 = 0 

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