Lesson 4: 8-2 Multiplying a Polynomial by a Monomial

How would you illustrate x and x^2?
How would you illustrate x^3?
How would 3x^3 look different from 3x^2?
Is it possible for a product of two polynomials to have a lower degree than either of the factors?

polynomial
monomial
distributive property
combine like terms
commutative property
associative property

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtarction, and multiplication; add, subtract, and multiply polynomials.

SAT questions related to polynomial operations: 7-3-2, 6-4-1, 4-3-5, 3-4-6, 1-3-5, 4-4-2, 3-4-33, 8-3-5;

The Distributive Property can be used to find the product of polynomial and monomial. Multiply each term of the polynomial by the monomial and simplify the product by combining like terms. Equations often contain polynomials that must be added, subtracted, or multiplied before they can be solved. Simplify each side and then apply the rules of solving multi-step equations.

Charmaine Brooks is opening a fitness club. She tells the contractor that the length of the fitness room should be three times the width plus 8 feet. To cover the floor with mats for exercise classes, Ms. Brooks needs to know the area of the floor. So she multiplies the width times the length, w(3w+8).

When a monomial is multiplied by a polynomial with three differnt degree terms, the reslult will be a polynomial with three terms. So if suddenly you only have twp terms, there must be an error.

Visual/special learning - Have students group algebra tiles to form a rectangle with a specific width and length, and then to write expression for for the area of the rectangle.

Practice: Exercises 1 -17

Exercises 51-54

McGraw Hill resources