Polynomials

College Algebra and TrigonometryCollege Algebra and Trigonometry

Dr.Maryam T. Al DossaryDr.Maryam T. Al Dossary

PolynomialsPolynomials

OBJECTIVES

At the end of this lesson, you should be able to:

1- Rewrite mathematical expressions using rules of

exponents

2- Implement arithmetic operations on polynomials

3- Find Special Products

Rules For Exponents

Zero Exponent

USING THE PRODUCT RULE

Find each product

Solution

Example1

(a) (b)

USING THE POWER RULES

Simplify, assume all variables represent nonzero real numbers

Solution

Example2

(a) (b) (c)

Evaluate each power

Solution

Example3

(a) (b) (a)

Polynomials

An algebraic expression is the result of adding, subtracting,

multiplying, dividing, raising to powers, or taking roots on any

combination of variables, such as x, y, m, a and b or constants such

as -2, 3, and 15.

A term the product of a real number and one or more variables

raised to powers

Like terms are terms with the same variables each raised to the

same powers

Polynomials

A polynomial is defined as a term or a finite sum of terms,

with only positive or zero integer exponents permitted on the

variables. (the terms of the polynomial cannot have variables

in a denominator)

Terms and Polynomials

The degree of a term with one variable is the exponent on

the variable

The degree of a polynomial is the greatest degree of any

term in a polynomial.

Types of Polynomials

ADDING AND SUBTRACTING POLYNOMIALS

Add or subtract as indicated

Solution

Example4

(a)

(b)

MULTIPLYING POLYNOMIALS

Find each product

Solution

Example4

(a)

(b)

Special Products

USING THE SPECIAL PRODUCTS

Find each product

Solution

Example5

(a)

(b)

DIVIDING POLYNOMIALS

Divide

Solution

Example6

DIVIDING POLYNOMIALS WITH

MISSING TERMSDivide

Solution

Example7

Thank You

Questions