Handout

Grade: 11

Course:Functions & Relations MCF3M

Team: 5

Algebra Skills: Multiplying Polynomials

Handout

Overview

The topic of this lesson is the multiplication of polynomials. It begins with a review of addition and subtraction of polynomials, and expanding polynomials. It then introduces the concept of multiplication of polynomials, beginning with monomials and proceeding to binomials. The lesson finishes with the multiplication of more complex polynomials, including trinomials and squared polynomials.

This handout first summarizes some of the basic concepts in this topic, and then presents three worked examples of increasing complexity. The examples are solved in a careful step-by-step manner, so that they can be easily followed. If these examples are fully understood, there should be no difficulties with either the homework or the test.

Tips

Definition of a polynomial:

A polynomial is an algebraic expression in the form ,

where:

  • the numerical coefficients are real numbers
  • and the exponents are non-negative integers

Special polynomials:

Definition / Examples
Monomial = a polynomial with one non-zero term / 2 , ,
Binomial = a polynomial with two terms / ,
Trinomial = a polynomial with three terms / ,

Degree of a polynomial:

Definition:The degree of a polynomial in one variable is the values of the highest exponent of the variable in the polynomial.

Examples

Polynomial / Degree of polynomial
2 / 0
+12 / 1
/ 5

Denominations

Definition / Examples
Constant = a polynomial in one variable of degree 0 / 7, -3.17
Linear polynomial = polynomial in one variable of degree 1 / ,
Quadratic polynomial = polynomial in one variable of degree 2 / ,
Cubic polynomial = polynomial in one variable of degree 3 /

2. Special products and exponent laws frequently necessary for working with polynomials

Special products / Exponent Laws

Problem 1

Multiply the two binomials.

Apply the distributive property, multiplying each

term in the first polynomial by each term in the

second polynomial.

Collect the like terms (same exponent).

Arrange the terms in decreasing order of the

exponents.

Problem 2

Multiply the two polynomials.

Apply the distributive property, multiplying each

term in the first polynomial by each term in the

second polynomial.

Collect the like terms (same exponent).

Arrange the terms in decreasing order of the

exponents.

Problem 3

Multiply the two polynomials.

Write the problem fully.

Apply the distributive property to each pair of

polynomials, multiplying each term in the first of

the pair by each term in the second of the pair.

Collect the like terms (same exponent) in each

polynomial.

Expand the polynomials.

Collect the like terms (same exponent).

Arrange the terms in decreasing order of the

exponents.

Anca Dragan, David KefferAlgebraic Skills

University of Ontario Institute of Technology Page1 of 3