In this Grade 11 enVision Algebra 2 lesson, students learn how to add, subtract, and multiply polynomials by applying the Commutative, Associative, and Distributive Properties to group and combine like terms. The lesson covers operations with both single- and multi-variable polynomials, introduces the concept of closure under polynomial addition and subtraction, and shows how polynomial multiplication can model real-world problems such as maximizing profit using a quadratic function.
Section 1
Add and Subtract Polynomials
To add or subtract polynomials, combine like terms. Like terms are monomials that have the same variables with the same exponents. The Commutative Property allows rearranging terms to group like terms together. When subtracting polynomials, be careful to distribute the negative sign to every term in the polynomial being subtracted.
Section 2
Products of polynomials
To find the product of two polynomials, multiply each term of the first polynomial by each term of the second polynomial, then combine any like terms.
If a product contains a monomial factor, it is a good idea to multiply the polynomial factors together first, and save the monomial factor for last.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
Add and Subtract Polynomials
To add or subtract polynomials, combine like terms. Like terms are monomials that have the same variables with the same exponents. The Commutative Property allows rearranging terms to group like terms together. When subtracting polynomials, be careful to distribute the negative sign to every term in the polynomial being subtracted.
Section 2
Products of polynomials
To find the product of two polynomials, multiply each term of the first polynomial by each term of the second polynomial, then combine any like terms.
If a product contains a monomial factor, it is a good idea to multiply the polynomial factors together first, and save the monomial factor for last.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter