Problem preview

A-APR.1 Warmup M2-001-A12-V02

Add, subtract, and multiply polynomials; understand polynomial closure under these operations.

Decide whether an expression is a polynomial in x

Problem

Determine whether \(x^{-1}~+~4\) is a polynomial in \(x\). Justify the classification using the requirements for exponents and coefficients.

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Yes. The exponent −1 is an integer, so it is allowed in a polynomial.

No. The exponent −1 is negative, so x−¹ is not a polynomial term.

Yes. The −1 is a negative coefficient on x, whose exponent is 1.

Yes. The valid constant 4 makes the whole expression a polynomial.

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Curriculum context

Course: Math II
Standard: A-APR.1
Category: Algebra
Domain: Arithmetic with Polynomials and Rational Expressions
Objective: Add, subtract, and multiply polynomials; understand polynomial closure under these operations.
Problem type: Decide whether an expression is a polynomial in x