Questions: 8x + 9/x + 9

Solution Steps

To determine if the expression \(8x + \frac{9}{x} + 9\) is a polynomial, we need to check if all the terms in the expression are polynomials. A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The term \(\frac{9}{x}\) can be rewritten as \(9x^{-1}\), which involves a negative exponent, indicating that the expression is not a polynomial.

The given expression is \(8x + \frac{9}{x} + 9\). We need to analyze each term to determine if the expression is a polynomial.

• The term \(8x\) is a polynomial term because it is a product of a constant and a variable raised to a non-negative integer power.
• The term \(\frac{9}{x}\) can be rewritten as \(9x^{-1}\), which involves a negative exponent. This indicates that it is not a polynomial term.
• The term \(9\) is a constant, which is a polynomial term.

For an expression to be a polynomial, all terms must be polynomial terms. Since \(\frac{9}{x}\) is not a polynomial term due to its negative exponent, the entire expression \(8x + \frac{9}{x} + 9\) is not a polynomial.

Final Answer