Question 691232
The key is recognizing that complex roots are generated in pairs.  So the roots are 13i, -13i, 5-10i, 5+10i.  In each case x= the root.  Subtract the root from both sides to find the factor.<P> 
x=13i so x-13i is the factor.  x=-13i so x+13i is the factor.  x=5-10i s0 x-5+10i is the factor.  x=5+10i so x-5-10i is the factor.<P>
You can multiply the factors together in any way, but generally it's best to multiply the factors based on the like roots together.  (x-13i)(x+13i)(x-5+10i)(x-5-10i).  Usually this solution is sufficient.  But you can multiply the factors.<P>
(x-13i)(x+13i) = x^2 +169.  The detailed explanation is after the problem solution.  Remember i^2 = -1.<P>
(x-5+10i)(x-5-10i)=x^2 -10x +125<P>
The two factors remaining are those answers (x^2 +169)(x^2 -10x +125)= x^4 -10x^3 +294x^2 -1690x +21125
<P>Hope the solution helped.  Sometimes you need more than a solution.  Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)


*[invoke explain_simplification "(x-13i)(x+13i)"]<P>
*[invoke explain_simplification "(x-5+10i)(x-5-10i)"]
*[invoke explain_simplification "(x^2 +169)(x^2 -10x +125)"]