Alright, let's examine the mathematical expression given:
[tex]\[ 9+4(x+2)-3x \][/tex]
To find the term that best describes "3" in this expression, we need to break it down and identify each part:
1. First term (9): This is a constant term because it does not change; it is simply the number 9.
2. Second term (4(x+2)): This term has a number 4 multiplied by a binomial expression [tex]\((x+2)\)[/tex]. The number 4 is a coefficient as it multiplies the expression.
3. Third term (-3x): Here, the number 3 is multiplied by the variable [tex]\(x\)[/tex]. The term is [tex]\(-3x\)[/tex], which signifies that 3 (specifically, the coefficient -3) is multiplied with the variable [tex]\(x\)[/tex].
Now, let's analyze the options:
A. Exponent: An exponent refers to the power to which a number or expression is raised (e.g., in [tex]\( x^2 \)[/tex], 2 is the exponent).
B. Constant: A constant is a number on its own, like 9, without any variables accompanying it. It does not change value.
C. Variable: A variable represents an unknown or changeable number, typically denoted by letters such as [tex]\(x\)[/tex], [tex]\(y\)[/tex], etc.
D. Coefficient: A coefficient is a numerical value placed before a variable, indicating how many times the variable is multiplied. In this case, 3 is multiplying [tex]\(x\)[/tex].
Thus, the number 3 in the term [tex]\(-3x\)[/tex] is the numerical factor multiplying the variable [tex]\(x\)[/tex].
Therefore, the correct answer is:
D. coefficient
