SOLUTION: I knew how to do these, but the expressions and the radicals confused me on this one. Please help! (the (radical) indicates where the square root sign is, on both threes)

Question 60930This question is from textbook College Algebra Graphs and Models
: I knew how to do these, but the expressions and the radicals confused me on this one. Please help!

(the (radical) indicates where the square root sign is, on both threes)

Find the polynomial function of degree 3 with the given numbers as zeros:

1-(radical)3,
1+(radical)3,
-2
Thank you This question is from textbook College Algebra Graphs and Models

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the polynomial function of degree 3 with the given numbers as zeros:
1 - SqRt(3),
1 + SqRt(3),
-2
:
The given 0,s also represent 3 factors of the function:
The last one, -2 is (x+2), right?
:
Regarding the other two, think of the doing completing the square in reverese:
:
x = 1 - SqRt(3)
x - 1 = -Sqrt(3)
:
Square both sides:
(x-1)^2 = -SqRt(3)* -SqRt(3), same as squaring +SqRt(3)
x^2 - 2x + 1 = 3
x^2 - 2x + 1 - 3 = 0
x^2 - 2x - 2 = 0
:
Mult the two factors:
(x+2)* (x^2 - 2x - 2) = (x^3 - 4x^2 + 2x + 4) is the function with the given 0's
:
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