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list rational zeros?

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2 Answers

a) Rational zeros = ±factors of 10 = ±1, ±2, ±5, ±10
 
b) f(-5) = f(1) = f(2) = 0
So, rational zeros are x = -5, 1, 2
 
c) f(x) = (x+5)(x-1)(x-2)
using synthetic division, possible zeroes are factors of 10 divided by factors of 1, the coefficient
of x^3, so we have +1, +2, +5, and +10
 
let's try 1
 
 
     1             1    2    -13    10
                          1       3   -10
                    1    3    -10     0   
                     
now divide x^3+2x^2-13x+10 by x-1                   
 
              
                   
 
                                x^2 + 3x - 10
                               ________________
                   (x-1)   / x^3+2x^2-13x+10
                            /   x^3-x^2
                              _________
                                       3x^2-13x
                                       3x^2-3x
                                      _________
                                              -10x+10
                                              -10x+10
                                              ________
                                                         0
  now factor x^2+3x-10 into (x+5)(x-2)
so we have (x-1)(x+5)(x-2) for the factorization and 1, -5, and 2 for the zeroes