SOLUTION: P(x)= x^3+x^2-4x+6 Express P(x) as a product of irreducible factors over the set of real numbers given that 1+i is a root of the polynomial. Thanks!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: P(x)= x^3+x^2-4x+6 Express P(x) as a product of irreducible factors over the set of real numbers given that 1+i is a root of the polynomial. Thanks!!       Log On


   

Question 942775: P(x)= x^3+x^2-4x+6
Express P(x) as a product of irreducible factors over the set of real numbers given that 1+i is a root of the polynomial.
Thanks!!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
1+i is a root of P(x) --> 1-i is also a root of P(x)

The sum of the roots of P(x) is -1, so (1+i) + (1-i) + r = -1 --> r = -3. So -3 is also a root of P(x) (you can check this).

Then P(x) = (x - (1+i))(x - (1-i))(x+3).