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Answer :
Certainly! Let's evaluate which of the given expressions is NOT a polynomial.
A polynomial is a mathematical expression consisting of variables (also known as indeterminates), coefficients, and exponents that are non-negative integers.
Let's look at each of the expressions one by one:
1. Expression 1: [tex]\(10x^7 - 9x^2 + 15x^3 + 9\)[/tex]
- Terms: [tex]\(10x^7, -9x^2, 15x^3, 9\)[/tex]
- All exponents (7, 2, 3, and 0 for the constant 9) are non-negative integers.
- Therefore, this is a polynomial.
2. Expression 2: [tex]\(9a^2 - 5\)[/tex]
- Terms: [tex]\(9a^2, -5\)[/tex]
- Both exponents (2 and 0 for the constant -5) are non-negative integers.
- Therefore, this is a polynomial.
3. Expression 3: 6
- This is a constant expression.
- A constant is considered a polynomial with degree 0.
- Therefore, this is a polynomial.
4. Expression 4: [tex]\(10x^{-7} - 9x^2 + 15x^3 + 9\)[/tex]
- Terms: [tex]\(10x^{-7}, -9x^2, 15x^3, 9\)[/tex]
- The first term [tex]\(10x^{-7}\)[/tex] has a negative exponent (-7).
- Polynomials cannot have negative exponents.
- Therefore, this is NOT a polynomial.
Based on this analysis, the expression that is NOT a polynomial is [tex]\(10x^{-7} - 9x^2 + 15x^3 + 9\)[/tex] because it contains a term with a negative exponent.
A polynomial is a mathematical expression consisting of variables (also known as indeterminates), coefficients, and exponents that are non-negative integers.
Let's look at each of the expressions one by one:
1. Expression 1: [tex]\(10x^7 - 9x^2 + 15x^3 + 9\)[/tex]
- Terms: [tex]\(10x^7, -9x^2, 15x^3, 9\)[/tex]
- All exponents (7, 2, 3, and 0 for the constant 9) are non-negative integers.
- Therefore, this is a polynomial.
2. Expression 2: [tex]\(9a^2 - 5\)[/tex]
- Terms: [tex]\(9a^2, -5\)[/tex]
- Both exponents (2 and 0 for the constant -5) are non-negative integers.
- Therefore, this is a polynomial.
3. Expression 3: 6
- This is a constant expression.
- A constant is considered a polynomial with degree 0.
- Therefore, this is a polynomial.
4. Expression 4: [tex]\(10x^{-7} - 9x^2 + 15x^3 + 9\)[/tex]
- Terms: [tex]\(10x^{-7}, -9x^2, 15x^3, 9\)[/tex]
- The first term [tex]\(10x^{-7}\)[/tex] has a negative exponent (-7).
- Polynomials cannot have negative exponents.
- Therefore, this is NOT a polynomial.
Based on this analysis, the expression that is NOT a polynomial is [tex]\(10x^{-7} - 9x^2 + 15x^3 + 9\)[/tex] because it contains a term with a negative exponent.
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