Your friend is incorrect in their classification of the terms "trinomial" and "binomial."
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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.
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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.
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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.
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