Identify like terms from a list of algebraic expressions.

1. Understand Like Terms: Like terms are terms that have the same variables raised to the same powers. The coefficients (the numbers in front of the variables) can be different.
2. Examine Each Term: We need to look at each term provided and identify its variable part (the variable and its exponent).
- $x^3$: Variable is $x$, exponent is 3.
- $-8$: This is a constant term, it has no variable part.
- $3x^2$: Variable is $x$, exponent is 2.
- $15x$: Variable is $x$, exponent is 1 (since $x$ is the same as $x^1$).
- $12x$: Variable is $x$, exponent is 1.
- $-x$: Variable is $x$, exponent is 1.
3. Identify Terms with the Same Variable Part: We are looking for terms that have the variable $x$ raised to the power of 1.
- $15x$ has $x^1$.
- $12x$ has $x^1$.
- $-x$ has $x^1$.
4. Select the Like Terms: The terms $15x$, $12x$, and $-x$ all have the variable $x$ raised to the power of 1. Therefore, they are like terms.
- $x^3$ is not a like term because the exponent is 3.
- $-8$ is not a like term because it is a constant and has no variable.
- $3x^2$ is not a like term because the exponent is 2.