Lesson 2: Multiplying Polynomials
Module 3: Polynomials
Lesson 2 Summary
In Lesson 2 you investigated the following questions:
- How is the distributive property extended to solve multiplication problems as well as other types of problems?
- How can you tell if two polynomials have been multiplied correctly?
In this lesson you learned to use the distributive property to multiply binomials. The distributive property is used to “pair” each term of one polynomial with another polynomial.
You learned that one way to keep track of which terms have been paired with others is by using a multiplication array.
You applied the strategies you learned in the previous lesson to multiply polynomials. These strategies included the use of a multiplication array, or area method, and the distributive property. While these strategies have different names, they are both based on the concept that each term of one polynomial is multiplied to each term of the second polynomial.
As the polynomials used in these calculations get bigger, so too does the risk of committing an error increase. Therefore, it is necessary to have a way of verifying that the solution is correct. You learned to verify a product by substituting a numerical value for x into both the original expression as well as the obtained product. If both resulting values were equal, then the product was verified to be correct.
In the Reflect and Connect section you explored other types of problems that can be solved by using a multiplication array and applying the concept of the distributive property. You realized the benefit of the array as a visualization tool that could help you to keep track of information. You have also learned that the distributive property is applicable to an assortment of mathematical problems, not only in the area of polynomials. You will continue to see these sorts of problems in future math courses.
Factoring is the next topic you will investigate. You can recover the factors of a polynomial by applying an appropriate factoring strategy. In the next lesson you will learn how to factor polynomials using the greatest common factor method. You will also begin exploring ways of factoring trinomials.