Polynomials
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces polynomials—algebraic expressions consisting of one or more terms with non-negative integer exponents. Students learn to identify monomials, binomials, and trinomials, understand degree, and distinguish polynomials from non-polynomial expressions.
Key Concepts
Property • A polynomial is a sum of terms, each of which is a power of a variable with a constant coefficient and a whole number exponent.
• The degree of a polynomial in one variable is the largest exponent that appears in any term.
• Like terms are any terms that are exactly alike in their variable factors. The exponents on the variable factors must also match.
Common Questions
What is a polynomial?
A polynomial is an algebraic expression with one or more terms, where variables have non-negative integer exponents. Examples include 3x^2 + 2x - 1 and 5.
What is the difference between a monomial, binomial, and trinomial?
A monomial has one term (like 4x^2), a binomial has two terms (like x + 3), and a trinomial has three terms (like x^2 + 5x + 6).
What is the degree of a polynomial?
The degree of a polynomial is the highest exponent of the variable in any of its terms. For example, 3x^4 + 2x - 1 has degree 4.
What expressions are NOT polynomials?
Expressions with variables in the denominator (like 1/x), under a radical (like sqrt(x)), or with fractional exponents are not polynomials.
Where are polynomials introduced in Grade 6?
Polynomials are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.