Final answer:
To create a trinomial with three different variables that has a total degree of 6, we can use terms such as x^4y^1z^1, x^3y^2z^1, and x^2y^2z^2, each of which sums to a degree of 6.
Step-by-step explanation:
To create a trinomial with three different variables that has a degree of 6, we need to consider that the degree of a term in a polynomial is the sum of the exponents of the variables in that term. Since we are looking for a trinomial, there will be three terms and we want the highest degree (the sum of exponents) of any term to be 6.
One possible trinomial could be:
x^4y^1z^1 + x^3y^2z^1 + x^2y^2z^2
In this trinomial, the degrees of the terms are as follows:
- First term: 4 (from x) + 1 (from y) + 1 (from z) = 6
- Second term: 3 (from x) + 2 (from y) + 1 (from z) = 6
- Third term: 2 (from x) + 2 (from y) + 2 (from z) = 6
All terms have a degree of 6, which is what we were aiming for, and we have used three different variables (x, y, and z).