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Answer :
Option D, x² + 2, is the correct answer because it is the only option that qualifies as a polynomial, which is defined by variables and coefficients involving only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
The question asks which of the listed options is a polynomial. A polynomial is a mathematical expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomials do not contain division by a variable, variables in the denominator, or negative exponents.
- Option A is not properly listed, so it cannot be evaluated.
- Option B similarly lacks proper listing for evaluation.
- Option C contains a negative exponent, which disqualifies it from being a polynomial because polynomials only have non-negative integer exponents.
- Option D, x² + 2, meets all criteria for a polynomial: it only involves addition and non-negative integer exponentiation of variables.
Therefore, Option D, x² + 2, is the correct answer because it is the only option that qualifies as a polynomial according to the definition of polynomials.
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Final answer:
A polynomial is an algebraic expression that consists of variables, coefficients, and exponents. The given polynomial is 7x² - 2x⁴ + 3x.
Explanation:
A polynomial is an algebraic expression that consists of variables, coefficients, and exponents. It can be written in the form:
anx^n + anx^(n-1) + ... + a2x^2 + a1x + a0
where n is a non-negative integer, a is a coefficient, and x is a variable raised to a non-negative integer exponent.
From the given options, the polynomial is 7x² - 2x⁴ + 3x (option C).
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