INTRODUCTION TO POLYNOMIALS. A monomial is a 1. 2. 3.______________of one or more numbers and variables. Examples:

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Presentation transcript:

INTRODUCTION TO POLYNOMIALS

A monomial is a ______________of one or more numbers and variables. Examples:

Why are the following NOT monomials? x + y 2 - 3a

What does each prefix mean? mono bi tri

What about poly? A ____________________ is a monomial, or a sum/difference of monomials. Each monomial is a __________. Important Note: An expression is not a polynomial if there is a variable in the denominator.

Special names are given to polynomials with two or three terms. A _____________ is a polynomial with two terms. A _____________ is a polynomial with three terms.

State whether each expression is a polynomial. If it is, identify it by the number of terms. 1) 7y - 3x + 4 2) 10x 3 yz 2 + 5x 3)

Which polynomial is represented by X2X2 1 1 X X X 1.x 2 + x x 2 + x x 2 + 2x x 2 + 3x No clue!

The degree of a monomial is the sum of the exponents of the variables. Ex.: Find the degree of each monomial. 1) 5x 2 2)4a 4 b 3 c 3)-3

The degree of a polynomial is the largest degree of the terms. Ex.: Find the degree of a polynomial. 1) 8x 2 - 2x + 7 Degrees: Which is largest? 2) y 7 + 6y 4 + 3x 4 m 4 Degrees:

Find the degree of x 5 – x 3 y

A polynomial is normally put in descending order. What is descending order?.

1)Put in descending order: 8x - 3x 2 + x ) Put in descending order in terms of x: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x

3) Put in descending order in terms of y: 12x 2 y 3 - 6x 3 y 2 + 3y - 2x 4)Put in descending order: 5a a - a 2

Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 1.x 4 + 4xy – x 3 y 2 – 2x 2 y 3 2.– 2x 2 y 3 – x 3 y 2 + 4xy + x 4 3.x 4 – x 3 y 2 – 2x 2 y 3 + 4xy 4.4xy – 2x 2 y 3 – x 3 y 2 + x 4

Classifying Polynomials By Degree DegreeNameExample

Non-Examples of Polynomials Fractions, Division Square Roots Variables as the exponent Negatives as the exponent Remember... these are NOT polynomials!

MonomialsBinomialsTrinomials