Let's carefully analyze the given expression:
[tex]\[ 9 + 4(x + 2) - 3x \][/tex]
1. Identify Components: We'll start by identifying the components of the expression:
- [tex]\( 9 \)[/tex]: This is a constant term.
- [tex]\( 4(x + 2) \)[/tex]: This term involves both a constant (4) multiplying a binomial expression ([tex]\(x + 2\)[/tex]).
- [tex]\(-3x\)[/tex]: This term involves a constant [tex]\(-3\)[/tex] multiplying a variable [tex]\( x \)[/tex].
2. Distribute and Simplify: Let's simplify the expression to make it clearer.
[tex]\[ 9 + 4(x + 2) - 3x \][/tex]
Applying distribution for [tex]\(4(x + 2)\)[/tex]:
[tex]\[ = 9 + 4x + 8 - 3x \][/tex]
Then we combine like terms:
[tex]\[ = (9 + 8) + (4x - 3x) \][/tex]
[tex]\[ = 17 + x \][/tex]
3. Identify the Term "3": Now, let's focus on the given term "3" in the original expression:
- Examining [tex]\(-3x\)[/tex], the term "3" is associated with the variable [tex]\(x\)[/tex].
- In this context, "3" represents the number that is multiplying the variable [tex]\(x\)[/tex], albeit with a negative sign in front of it ([tex]\(-3\)[/tex]). The term for such a number is known as the coefficient.
4. Conclusion: The term "3" is the part of the expression [tex]\(\-3x\)[/tex] that multiplies the variable [tex]\( x \)[/tex]. Therefore, "3" is best described as the coefficient.
So, the correct answer is:
C. coefficient.
