Which statement defines a polynomial?

Which statement defines a polynomial?

• A. A polynomial is a monomial or a sum or difference of monomials.
• B. A polynomial is only a monomial.
• C. A polynomial is a product of polynomials.
• D. A polynomial is a fraction with polynomial numerator and denominator.

Answer: (A)

A polynomial is built from monomials by adding or subtracting them. Each term is a monomial—a constant times variables raised to nonnegative integer powers—and a polynomial is just a finite sum (or difference) of those monomials. This means a polynomial can be a single monomial, like 7x^3, or a combination such as x^2 + 3x − 5, where each part is a monomial and the parts are added or subtracted. That’s why the statement that defines a polynomial as a monomial or a sum or difference of monomials is the best description. It captures both the single-term case and the way multiple terms come together. The other ideas aren’t right because they either impose too strict a limit (polynomials can have more than one term) or describe a broader class (products of polynomials, which can be polynomials only after expansion) or a different kind of function (fractions with polynomial numerator and denominator, which are usually rational functions, not polynomials).

A polynomial is built from monomials by adding or subtracting them. Each term is a monomial—a constant times variables raised to nonnegative integer powers—and a polynomial is just a finite sum (or difference) of those monomials. This means a polynomial can be a single monomial, like 7x^3, or a combination such as x^2 + 3x − 5, where each part is a monomial and the parts are added or subtracted.

That’s why the statement that defines a polynomial as a monomial or a sum or difference of monomials is the best description. It captures both the single-term case and the way multiple terms come together.

The other ideas aren’t right because they either impose too strict a limit (polynomials can have more than one term) or describe a broader class (products of polynomials, which can be polynomials only after expansion) or a different kind of function (fractions with polynomial numerator and denominator, which are usually rational functions, not polynomials).