The expression has a coefficient of 1 when simplified C. Nate. Therefore , C. Nate is correct .
A coefficient is the numerical factor in a term of a polynomial. For example, in the term 3x, the coefficient is 3.
When simplifying an expression, we combine like terms. Like terms are terms that have the same variables raised to the same powers.
For example, the terms 2x and 3x are like terms.
To simplify Nate's expression, we combine the constant terms:
7+(x+1) = 7 + x + 1 = x + 8
Now, the expression has only one term, which is x. The coefficient of the term x is 1.
Detailed explanation of each student's expression:
Hunter: 5(3x+2)+1
This expression can be simplified as follows:
5(3x+2)+1 = 15x + 10 + 1 = 15x + 11
The coefficient of the term x is 15, not 1.
Michael: 6x-1+5x
This expression can be simplified as follows:
6x-1+5x = 11x - 1
The coefficient of the term x is 11, not 1.
Spencer: (2x-2)+2
This expression can be simplified as follows:
(2x-2)+2 = 2x + 0 = 2x
The coefficient of the term x is 2, not 1.
Therefore, Nate's expression has a coefficient of 1 when simplified.