Learn on PengienVision, Algebra 1Chapter 7: Polynomials and Factoring

Lesson 1: Adding and Subtracting Polynomials

In this Grade 11 enVision Algebra 1 lesson, students learn to identify and classify monomials and polynomials by degree and number of terms, write polynomials in standard form, and combine like terms to add and subtract polynomial expressions. The lesson introduces key vocabulary including the degree of a monomial, degree of a polynomial, and the Closure Property, building the foundational skills needed for factoring in Chapter 7.

Section 1

What is a polynomial?

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 4x3+2x2−7x+54x^3 + 2x^2 - 7x + 5 is a polynomial.
  • The expression 2+6x2 + \frac{6}{x} is not a polynomial because a variable appears in the denominator.

Section 2

Identifying Polynomials

Property

A monomial is a term of the form axmax^m, where aa is a constant and mm is a whole number.
A monomial, or two or more monomials combined by addition or subtraction, is a polynomial.
A polynomial with exactly one term is called a monomial.
A polynomial with exactly two terms is called a binomial.
A polynomial with exactly three terms is called a trinomial.

Examples

  • 15x415x^4 is a monomial because it has one term.
  • y2−25y^2 - 25 is a binomial because it has two terms.
  • 3a2−6a+93a^2 - 6a + 9 is a trinomial because it has three terms.

Explanation

Think of polynomials as a family. Monomials (one term), binomials (two terms), and trinomials (three terms) are specific members. We use these names for them, and call everything else with more than three terms a polynomial.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

What is a polynomial?

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 4x3+2x2−7x+54x^3 + 2x^2 - 7x + 5 is a polynomial.
  • The expression 2+6x2 + \frac{6}{x} is not a polynomial because a variable appears in the denominator.

Section 2

Identifying Polynomials

Property

A monomial is a term of the form axmax^m, where aa is a constant and mm is a whole number.
A monomial, or two or more monomials combined by addition or subtraction, is a polynomial.
A polynomial with exactly one term is called a monomial.
A polynomial with exactly two terms is called a binomial.
A polynomial with exactly three terms is called a trinomial.

Examples

  • 15x415x^4 is a monomial because it has one term.
  • y2−25y^2 - 25 is a binomial because it has two terms.
  • 3a2−6a+93a^2 - 6a + 9 is a trinomial because it has three terms.

Explanation

Think of polynomials as a family. Monomials (one term), binomials (two terms), and trinomials (three terms) are specific members. We use these names for them, and call everything else with more than three terms a polynomial.