Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is a polynomial in algebra?

1. An expression that includes fractions of variables

2. An expression solely consisting of constants

3. An expression that consists of variables raised to whole number exponents combined with coefficients

4. An equation that has no variables

The correct answer is: An expression that consists of variables raised to whole number exponents combined with coefficients

A polynomial in algebra is defined as an expression that consists of variables raised to whole number exponents, combined with coefficients. This definition is central to understanding polynomials because they can involve multiple variables and terms, as long as the exponents of the variables are non-negative integers. For instance, expressions such as 3x^2 + 2x - 5 and 4ab^3 + 5a^2 are both examples of polynomials because they adhere to this structure. Each term in a polynomial is made up of a coefficient (a constant multiplying the variable) and a variable component that is raised to a whole number exponent. This definition distinguishes polynomials from other types of algebraic expressions. For example, if an expression includes fractions of variables or negative exponents, it does not meet the criteria for being classified as a polynomial. Similarly, while constants are part of polynomial terms, an expression consisting solely of constants, or one that contains no variables at all, does not fit the broader definition of a polynomial. Thus, option C correctly encapsulates the key characteristics of polynomials in algebra.