SOLUTION: The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with

Question 92463This question is from textbook Algebra and Trigonometry
: The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. This question is from textbook Algebra and Trigonometry

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The degree three polynomials f(x) with real coefficients and leading coefficent 1, has 4 and 3+i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
:
Factor when x = 4: (x-4)
:
Expression when x = 3 + i:
x - 3 = i; subtracted 3 from both sides
:
(x-3)^2 = i^2; squared both sides
:
x^2 - 6x + 9 = -1; FOILed (x-3)(x-3), i^2 = -1
:
x^2 - 6x + 9 + 1 = 0; added 1 to both sides
:
x^2 - 6x + 10 = 0
:
Product of a linear and quadratic:
(x-4) * (x^2 - 6x + 10) = (x^3 - 10x^2 + 34x - 40) = f(x)
:
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