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}