Hi,

The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0

roots -1+4i and -1-4i

f(x) = a(x-(-1+4i))(x -(-1-4i)) = a(x^2 -2x +17)

 a = 1

f(x) = x^2 -2x +17

Check product  Using FOIL

F	First terms

O	Outside terms

I	Inside terms

L	Last terms

 

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
 



a quadratic equation could be found with roots like this: Write the roots, a and b, in the form (x-a)(x-b).







given:  and ..plug it in











































 

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