SOLUTION: How do you factor a Polynomial with imaginary roots? I need to factor this 9x^6-26x^5-57x^4+201x^3+68x^2-445x-50 One of the solutions is 2-i

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you factor a Polynomial with imaginary roots? I need to factor this 9x^6-26x^5-57x^4+201x^3+68x^2-445x-50 One of the solutions is 2-i      Log On


   

Question 1554: How do you factor a Polynomial with imaginary roots? I need to factor this
9x^6-26x^5-57x^4+201x^3+68x^2-445x-50 One of the solutions is 2-i
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let p(x) =9x^6-26x^5-57x^4+201x^3+68x^2-445x-50
Since complex roots should be in conjugates form ,if one is 2-i, another is 2+i.
And so, (x -2+i)(x -2-i) = x^2 -4x + 5 must be a factor of p(x).
Use long division p(x)/(x^2 -4x + 5)= 9x^4 +10x^3 -62x^2 -97x-10
and then you can find (x+2) and (9x+1) are factors
of p(x).
Finally, p(x) = (x+2)(9x+1)(x^2 -x - 5)( x^2 -4x + 5)