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The question in the image asks whether the algebraic expression \( \frac{6x + 9}{x} \) is a polynomial, and if so, to write it in standard form.

Let's break it down:

The expression given is \( \frac{6x + 9}{x} \). This can be simplified by dividing each term in the numerator by \( x \):
\[
\frac{6x}{x} + \frac{9}{x} = 6 + \frac{9}{x}
\]

Now, check if the result is a polynomial:
- The term "6" is a constant, which is part of a polynomial.
- The term \( \frac{9}{x} \) involves division by a variable \( x \), which is not allowed in a polynomial. A polynomial cannot have variables in the denominator.

Therefore, the given expression is **not** a polynomial because of the term \( \frac{9}{x} \), which introduces a negative exponent (\( x^{-1} \)).

Would you like further clarification or details? Here are five related questions to expand your understanding:

1. What are the conditions for an expression to be classified as a polynomial?
2. How do rational expressions differ from polynomials?
3. Can you give examples of expressions that look similar to polynomials but aren't?
4. How can negative or fractional exponents affect polynomial classification?
5. What are some real-world applications of polynomials in mathematics?

**Tip:** A polynomial is made up of terms where the exponents of the variables are non-negative integers. Any division by a variable disqualifies the expression from being a polynomial.

Is the algebraic expression 6x + 9 / x a polynomial? If it is, write the polynomial in standard form.

Explore whether the algebraic expression (6x + 9) / x is a polynomial. Learn how to simplify it and check for polynomial classification by examining its terms. This problem is ideal for students in Grades 8-10.

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