1. **State the problem:** Identify the true statements about the algebraic expression $5x + 1 + 2y$. 2. **Analyze the expression:** The expression is $5x + 1 + 2y$. 3. **Check each statement:** - $5x + 1 + 2y$ is written as a sum of three terms: The terms are $5x$, $1$, and $2y$. This is true. - $5x + 1 + 2y$ is written as a product of three factors: The expression is a sum, not a product. This is false. - $2$ is a coefficient: In $2y$, $2$ multiplies $y$, so $2$ is a coefficient. This is true. - $1$ is a constant: $1$ is a number without a variable, so it is a constant. This is true. - $2y$ and $1$ are like terms: Like terms have the same variable part. $2y$ has variable $y$, $1$ has none, so they are not like terms. This is false. - None of these are true: Since some statements are true, this is false. **Final true statements:** - $5x + 1 + 2y$ is written as a sum of three terms. - $2$ is a coefficient. - $1$ is a constant.