Question
2. Your friend tells you that 5x + 6y - 7z is a trinomial, but 2x2 + 3x - 5 is a binomial. Is your friend correct? Why or why not? Explain.(3 marks
Answers
Answered by
GPT-4o mini
Your friend is incorrect in their classification of the terms "trinomial" and "binomial."
1. **Definition of Terms**:
- A **trinomial** is an algebraic expression that contains three terms. For example, \(a + b + c\) is a trinomial.
- A **binomial** is an algebraic expression that contains two terms. For example, \(a + b\) is a binomial.
2. **Analysis of the Expressions**:
- The expression **5x + 6y - 7z** contains three distinct terms: \(5x\), \(6y\), and \(-7z\). Therefore, it is correctly identified as a **trinomial**.
- The expression **2x^2 + 3x - 5** also contains three terms: \(2x^2\), \(3x\), and \(-5\). Thus, it should be classified as a **trinomial**, not a binomial.
3. **Conclusion**:
Your friend mistakenly stated that \(2x^2 + 3x - 5\) is a binomial when it is, in fact, a trinomial. Therefore, both of their classifications were incorrect regarding the second expression.
1. **Definition of Terms**:
- A **trinomial** is an algebraic expression that contains three terms. For example, \(a + b + c\) is a trinomial.
- A **binomial** is an algebraic expression that contains two terms. For example, \(a + b\) is a binomial.
2. **Analysis of the Expressions**:
- The expression **5x + 6y - 7z** contains three distinct terms: \(5x\), \(6y\), and \(-7z\). Therefore, it is correctly identified as a **trinomial**.
- The expression **2x^2 + 3x - 5** also contains three terms: \(2x^2\), \(3x\), and \(-5\). Thus, it should be classified as a **trinomial**, not a binomial.
3. **Conclusion**:
Your friend mistakenly stated that \(2x^2 + 3x - 5\) is a binomial when it is, in fact, a trinomial. Therefore, both of their classifications were incorrect regarding the second expression.