SOLUTION: The third degree polynomial f(x) with real coefficients and leading coefficient1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials wi

Question 46349: The third degree polynomial f(x) with real coefficients and leading coefficient1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
(x - 4)(x - (3 + i))(x - (3 - i))
(x - 4)((x - 3) + i)((x - 3) - i)
(x - 4)((x - 3)^2 + 1)
(x - 4)(x^2 - 6x + 9 + 1)
(x - 4)(x^2 - 6x + 10)
x^3 - 4x^2 - 6x^2 + 24x + 10x - 40
x^3 - 10x^2 + 34x - 40 = f(x)

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