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