### Instruction: Factor the following expression: $55z^{17}+121z^{34}$.### Response: I notice that both terms have a factor of $z^{17}$, so I can factor that out first: $z^{17}(55+121z^{17})$.
Now I have to factor the remaining expression inside the parentheses: $55+121z^{17}$.
I see that both coefficients are divisible by 11, so I can factor that out as well: $z^{17}(11)(5+11z^{17})$.
Finally, I check if the expression $5+11z^{17}$ is factorable further.
I realize that it is a sum of two terms, and there is no common factor or easy way to factor it by grouping or using a special formula.
So, I conclude that it is irreducible, and I have factored the expression completely.