Final answer:
There is no error in the terms 4x², 6x², 18x², or x² as part of the quotient of the expression 4x + 6x² + 18x + 78 + x − 3 since the simplification combines like terms to produce 6x² + 23x + 75.
Step-by-step explanation:
The student is asking which term in the polynomial expression 4x + 6x² + 18x + 78 + x − 3 contains an error when referring to a quotient. This seems to be a question about simplifying and combining like terms, rather than about division into a quotient. First, we need to combine like terms in the expression. The terms 4x and 18x and x can be combined, because they all contain the variable x to the power of 1. Likewise, we have a constant term of 78 and -3 that can be combined. The term 6x² is already in its simplest form as there are no other x² terms to combine it with.
The correct simplification process would be:
- Combine 4x, 18x, and x to get 23x.
- Combine 78 and -3 to get 75.
- Recognize that 6x² has no like terms, so it stays as is.
Therefore, the correctly simplified expression is 6x² + 23x + 75.
Considering the original terms provided in the question (A) 4x², (B) 6x², (C) 18x², and (D) x², none of these precisely match a term from the correctly simplified expression; there is no x² term in front of 23x. Hence, there seems to be a misunderstanding as there are no separate x² terms—there is only a single 6x² term in the correct simplification. As such, without additional context, the error in the terms listed cannot be determined, unless it is the misunderstanding that separate x² terms exist after simplification.