To accurately determine which statement describes the expression [tex]\(\frac{x-2}{x^2+9}\)[/tex], let's analyze each option carefully:
1. Option A: The product of [tex]\(x-2\)[/tex] and [tex]\(x^2+9\)[/tex]
- The term "product" refers to multiplication. If we were talking about the product of [tex]\(x-2\)[/tex] and [tex]\(x^2+9\)[/tex], then the expression would be [tex]\((x-2) \cdot (x^2+9)\)[/tex]. This does not match our given expression, which is a division.
2. Option B: The quotient of [tex]\(x^2+9\)[/tex] and [tex]\(x-2\)[/tex]
- The term "quotient" refers to division. Here, it describes [tex]\( \frac{x^2+9}{x-2} \)[/tex], which is the division of [tex]\(x^2+9\)[/tex] by [tex]\(x-2\)[/tex]. This is the reverse of our given expression and, hence, does not match.
3. Option C: The quotient of [tex]\(x-2\)[/tex] and [tex]\(x^2+9\)[/tex]
- Again, "quotient" denotes division. This statement describes [tex]\(\frac{x-2}{x^2+9}\)[/tex], which is exactly our given expression. This option matches perfectly.
4. Option D: The product of [tex]\(x^2+9\)[/tex] and [tex]\(x-2\)[/tex]
- Similar to Option A, this refers to the multiplication [tex]\((x^2+9) \cdot (x-2)\)[/tex]. Since our expression is a division and not a multiplication, this option does not match.
Based on this detailed analysis, the correct statement that accurately describes the expression [tex]\(\frac{x-2}{x^2+9}\)[/tex] is:
C. The quotient of [tex]\(x-2\)[/tex] and [tex]\(x^2+9\)[/tex]
