I have a maple program that generates a polynomial g(y)=(80y^8 + 68y^6 + 12y^4 -4y^2 -1). This polynomial has two real roots (irrational roots), call them +/- y*. My code does a sequential calculation, and often sI am left with a higher order polynomial in y that has the form h(y)= p(y)*g(y), where p(y) is also a polynomial in y. This polynomial h(y)=p(y)*g(y) is not in factored form (i.e. it would look like expand(p(y)*g(y)). Is there a way to instruct maple to recoginize that +/-y* is also a root h(y)=p(y)*g(y)? So far I've tried things like applyrule([g(y*)=0],h(y*)), but nothing seems to work (I suspect because Maple cannot recgonize that g(y) is a factor of h(y)). I am not interested in computing this numerically. I am just trying to find a way to instruct Maple to recognize symbolically that h(y*) =0.
Thanks a million for anyone who has any idea.