What is a polynomial?
What is a Polynomial? introduces the formal definition: a polynomial is an algebraic expression made of terms where each term is a power of a variable with a constant coefficient and whole-number exponents. Covered in Yoshiwara Elementary Algebra Chapter 7: Polynomials, Grade 6 students learn to classify polynomials (monomial, binomial, trinomial) and recognize what expressions qualify as polynomials versus those that do not (such as those with negative or fractional exponents). This foundation supports all future work with polynomial operations and factoring.
Key Concepts
Property A polynomial is an algebraic expression with several terms. Each term is a power of a variable (or a product of powers) with a constant coefficient. The exponents in a polynomial must be whole numbers, which means that a polynomial has no radicals containing variables, and no variables in the denominators of fractions.
Examples The expression $4x^3 + 2x^2 7x + 5$ is a polynomial.
The expression $2 + \frac{6}{x}$ is not a polynomial because a variable appears in the denominator.
Common Questions
What is a polynomial?
A polynomial is an algebraic expression with one or more terms, where each term is a constant multiplied by a variable raised to a non-negative whole number exponent. Examples include 3x², x³ + 2x - 5, and 7.
What is the difference between a monomial, binomial, and trinomial?
A monomial has one term (like 4x²), a binomial has two terms (like x + 3), and a trinomial has three terms (like x² + 5x + 6).
Can a polynomial have fractional exponents?
No. Polynomials only allow non-negative integer (whole number) exponents. Expressions like x^(1/2) or x^(-1) are not polynomials.
Where is what is a polynomial in Yoshiwara Elementary Algebra?
The definition and classification of polynomials is in Chapter 7: Polynomials of Yoshiwara Elementary Algebra.
Is a constant like 5 a polynomial?
Yes. A constant is a polynomial of degree 0, since it can be written as 5x⁰.