SOLUTION: Use the rational zeros and synthetic division to factor f(x)=x^3+x^2-5x-2.

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Question 365546: Use the rational zeros and synthetic division to factor f(x)=x^3+x^2-5x-2.
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use the rational zeros and synthetic division to factor f(x)=x^3+x^2-5x-2.
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Graphing I found a rational zero at x = 2
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Using synthetic division you can find the following:
2)....1....1....-5....-2
.......1....3.....1..|..0
Quotient: x^2+3x+1
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Use the Quadratic formula to find the other zeroes:
x = [-3 +- sqrt(9-4*1*1)]/2
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x = [-3 +- sqrt(5)]/2
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x = (-3+sqrt(5))/2 or x = (-3-sqrt(5))/2
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Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

*Note: exploring the factors of -2, found that x = 2 works       



          x^2 + 3x + 1

        __________________________

x - 2 | x^3 +  x^2  - 5x  -  2

      - (x^3 -2x)

       ---------------

                3x -  5x

             - (3x -  6x)

                ---------

                      x  - 2

                  - ( x  - 2)

                     ---------

                           0

x^2 + 3x + 1

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-3+%2B-+sqrt%28+5+%29%29%2F%282%29+

x = 2 and x+=+%28-3+%2B-+sqrt%28+5+%29%29%2F%282%29+