Question

2. Your friend tells you that 5x + 6y - 7z is a trinomial, but 2 times 2 + 3x - 5 is a binomial. Is your friend correct? Why or why not? Explain.(3 marks

Answer 1

Your friend is incorrect in both assertions. Let's break it down:

1. **5x + 6y - 7z**:
- A trinomial is defined as a polynomial with three terms. In this case, 5x, 6y, and -7z are indeed three distinct terms. Therefore, 5x + 6y - 7z is a trinomial, and this part of your friend's statement is correct.

2. **2 times 2 + 3x - 5**:
- First, let's evaluate the expression. The phrase "2 times 2" equals 4, so the expression simplifies to:
\[
4 + 3x - 5
\]
- Further simplifying this gives:
\[
3x - 1
\]
- Now, we can count the terms. This expression has two terms: \(3x\) and \(-1\). Thus, it is a binomial, which is correct.

However, the confusion likely arises from what is considered when classifying polynomials. Your friend describes \(2 \cdot 2 + 3x - 5\) simply as a binomial without correctly summarizing the simplification. So, technically, while the second statement can be seen as a binomial, it is worth noting that the original way it was presented (before simplification) was misleading.

To sum up:
- **5x + 6y - 7z** is indeed a trinomial (correct).
- **2 times 2 + 3x - 5** evaluates to a binomial (correct due to simplification) but presented in a confusing manner initially.

Overall, your friend's assertion regarding the trinomial is correct, but the way the binomial was introduced could lead to misunderstandings without clarification through simplification.