Final answer:
The example of scratch work that is not reversible is taking square roots of a number, as it introduces ambiguity with both positive and negative solutions.
Step-by-step explanation:
The question asks which of the following is an example of when scratch work is not reversible:
- Solving linear equations
- Simplifying algebraic expressions
- Dividing polynomials
- Taking square roots of a number
Most mathematical operations used in problems like simplifying algebraic expressions, solving linear equations, or dividing polynomials are reversible. For example, operations such as addition, subtraction, multiplication, and division have their inverse operations.
However, when we take the square root of a number, we encounter a scenario that is not as straightforward to reverse because it does not guarantee a single unique answer. When you square root a number, you get a positive and a negative result (since both can be squared to give the original number), which means the process has more than one possible inverse. This makes the square root operation in general an example of when scratch work is not reversible, as it does not uniquely determine the original value before taking the square root.