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)   (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
---
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)   (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 = 2 and 



 

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