Question 74257
<pre>
List all of the possible rational zeros of f(x)=3x^5-7x^3+2x-15.


To find the list of all possible rational zeros of f(x)=3x^5-7x^3+2x-15,
p/q will help you. p = the factors of the last term 15
                   q = the factors of the coefficient of the first term

p = 15 = 15, 1, -15, -1, 3,5, -3,-5
q = 3  = 3,1, -3,-1

List of possible rational zeros 
 p     15             p      15             p     15           p     15 
___ = ____ = 5      ____ = _____ = 15     ____ = ____ = -15   ___ = _____ = -5
 q      3             q      1              q     -1           q      -3


p       1             p       1             p      1           p      1  
___ = ____          ____ = _____ = 1       ____ = ____ = -1   ___ = _____ 
 q      3             q      1              q     -1           q      -3


p     -15             p     -15             p     -15          p     -15 
___ = ____ = -5      ____ = _____ = -15   ____ = ____ =  15   ___ = _____ = 5
 q      3             q      1              q     -1           q      -3


p     -1             p      -1             p     -1           p     -1      1
___ = ____          ____ = _____ = -1    ____ = ____ = 1     ___ = _____ = ___
 q      3             q      1              q    -1           q      -3     3



p      3             p       3             p      3           p      3
___ = ____ = 1      ____ = _____ = 3     ____ = ____ = -3    ___ = _____ = -1
 q      3             q      1              q     -1           q    -3

p      -3             p       -3             p     -3           p      -3
___ = ____ = -1      ____ = _____ = -3     ____ = ____ =  3    ___ = _____ = 1
 q      3             q      1              q     -1           q       -3

p       5             p       5             p      5           p      5
___ = ____           ____ = _____ = 5     ____ = ____ = -5    ___ = _____ 
 q      3             q      1              q     -1           q      -3

 
p       -5            p      -5             p     -5           p      -5     5
___ = ____           ____ = _____ = -5    ____ = ____ =  5    ___ = _____ = ___
 q      3             q      1              q     -1           q      -3     3


Then you can find all the possible rational zeros now
{1,3,-3,-1,-1/3,1/3, 5, -15, 15, 5, 5/3, -5/3}