https://file.aiquickdraw.com/mathbot/file/1726253518292wmday49g.jpg

The problem asks to consider the expression \( 5(9 + 4)(3x + 8) \) and select all of the true statements below. Let's analyze the options step by step:

1. **Statement:** "(3x + 8) is written as a sum of three terms."
   - **Explanation:** The expression \( 3x + 8 \) has **two terms**: \( 3x \) and 8. It is a binomial, not a trinomial (which would have three terms). 
   - **Conclusion:** This statement is **false**.

2. **Statement:** "In \( 3x \), 3 is a coefficient."
   - **Explanation:** The coefficient in a term is the number multiplied by the variable. In \( 3x \), the coefficient of \( x \) is indeed 3.
   - **Conclusion:** This statement is **true**.

3. **Statement:** "In \( (3x + 8) \), 3x is a constant."
   - **Explanation:** A constant is a number without a variable. \( 3x \) contains a variable \( x \), so it is not a constant but a term with a variable.
   - **Conclusion:** This statement is **false**.

4. **Statement:** "9 and 4 are like terms."
   - **Explanation:** Like terms are terms that have the same variables raised to the same power. Here, both 9 and 4 are constants (no variables), so they are like terms.
   - **Conclusion:** This statement is **true**.

5. **Statement:** "5 is a factor."
   - **Explanation:** In the expression \( 5(9 + 4)(3x + 8) \), the number 5 is multiplying the entire expression, meaning it is a factor of the whole expression.
   - **Conclusion:** This statement is **true**.

6. **Statement:** "None of these are true."
   - **Explanation:** Some of the statements are true, so this option is incorrect.
   - **Conclusion:** This statement is **false**.

### Final Answer:
The true statements are:
- "In \( 3x \), 3 is a coefficient."
- "9 and 4 are like terms."
- "5 is a factor."

Would you like more details or clarifications on any of these points?

### Related Questions:
1. How do you determine if two terms are "like terms"?
2. What does it mean for a number to be a factor in an expression?
3. How do you identify the coefficient in a term with a variable?
4. Can \( 3x + 8 \) be factored further?
5. What is the difference between a binomial and a trinomial?

### Tip:
Always remember that constants are terms without variables, while coefficients are the numerical part of terms with variables.

Consider the following expression: 5(9 + 4)(3x + 8). Select all of the true statements below.

Explore the algebraic expression 5(9 + 4)(3x + 8) and select the correct true statements, including understanding coefficients, constants, and factors. Suitable for Grades 6-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation