(a) Given , , and , Let a=3x, b=5y, and x=-6z Determine the monic cubic polynomial in terms of a variable whose roots

(a) Given  \(3x+5y-6z=2\), \(5xy-10yz-6xz=-41\) , and\(xyz=6\) , 
Let a=3x, b=5y, and x=-6z
Determine the monic cubic polynomial in terms of a variable  whose roots are t=a, t=b, and t=c. Make sure to enter your answer in terms of t and only t, in expanded form.

 

(b) Given that (x, y, z) is a solution to the original system of equations, determine all distinct possible values of x+y.