Is it valid to use the rational root theorem on a polynomial with variable integer coefficients? Does it change anything if you have constraints making the variables interdependent?
For example, can I use the rational root theorem with:
d6+4dm9−10dv6m6+15dv12m3−8dv18+27v3m3to say d can only take rational integer values of factors of 27v3m3 when d,v,m are known integers?
What if I have constraint equations such that they covary? Such as b=d21v3m6 where b is another variable also known to be an integer, or more constraint equations.
For example, can I use the rational root theorem with:
d6+4dm9−10dv6m6+15dv12m3−8dv18+27v3m3to say d can only take rational integer values of factors of 27v3m3 when d,v,m are known integers?
What if I have constraint equations such that they covary? Such as b=d21v3m6 where b is another variable also known to be an integer, or more constraint equations.