Which description best defines a polynomial function?

Which description best defines a polynomial function?

• A. A function with a single term
• B. A function with multiple terms and multiple powers of x
• C. A function that is always rational
• D. A function with only square roots

Answer: (B)

A polynomial function is formed by adding terms that each look like a coefficient times x raised to a nonnegative integer power. This means you can have several terms, each with its own power of x, as in 3x^3 + 2x^2 - x + 7. That description—having multiple terms and multiple powers—best captures the typical polynomial form because it includes the common case of many terms with various powers. Note that a polynomial can also be a single-term expression like 5x^4 and is still a polynomial, but the standard idea is a sum of such terms with nonnegative integer exponents. Polynomials are not constrained to produce only rational values for every x, and they do not involve square roots as their defining feature, so those descriptions aren’t accurate.

A polynomial function is formed by adding terms that each look like a coefficient times x raised to a nonnegative integer power. This means you can have several terms, each with its own power of x, as in 3x^3 + 2x^2 - x + 7. That description—having multiple terms and multiple powers—best captures the typical polynomial form because it includes the common case of many terms with various powers. Note that a polynomial can also be a single-term expression like 5x^4 and is still a polynomial, but the standard idea is a sum of such terms with nonnegative integer exponents. Polynomials are not constrained to produce only rational values for every x, and they do not involve square roots as their defining feature, so those descriptions aren’t accurate.