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Polynomials
Finding the Greatest Common Factor
Factoring Trinomials
Absolute Value Function
A Summary of Factoring Polynomials
Solving Equations with One Radical Term
Adding Fractions
Subtracting Fractions
The FOIL Method
Graphing Compound Inequalities
Solving Absolute Value Inequalities
Adding and Subtracting Polynomials
Using Slope
Solving Quadratic Equations
Factoring
Multiplication Properties of Exponents
Completing the Square
Solving Systems of Equations by using the Substitution Method
Combining Like Radical Terms
Elimination Using Multiplication
Solving Equations
Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
Solving Quadratic Equations
Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
Solving Compound Linear Inequalities
Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
Multiplying and Dividing Signed Numbers
Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 
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Polynomials

After studying this lesson, you will be able to:

  • Find the degree of a polynomial.
  • Classify polynomials.
  • Put polynomials in descending order.

A Polynomial is a monomial or a sum of monomials.

There are 3 Special Names of Polynomials :

Monomials: have one term

Binomials: have two terms

Trinomials: have three terms

**Remember that terms are separated by + and - signs**

 

Example 1

Classify the polynomial as a monomial, a binomial, or a trinomial: 3xy

Since this polynomial has one term, it is a monomial .

 

Example 2

Classify the polynomial as a monomial, a binomial, or a trinomial: -2x + 4

Since this polynomial has two terms, it is a binomial.

 

Example 3

Classify the polynomial as a monomial, a binomial, or a trinomial: x 2 + 2x - 4

Since this polynomial has three terms, it is a trinomial .

 

Example 4

Classify the polynomial as a monomial, a binomial, or a trinomial: - 2 x y 2 z 3

Since this polynomial has one term, it is a monomial.

 

Degree of a Term is the sum of the exponents of the variables.

The Degree of a Polynomial is the highest degree of its terms.

 

Example 5

Identify the degree of each term and the degree of the polynomial: - 2 x y 2 z 3

This polynomial has one term. To find the degree of the term, we add the exponents of the variables. The variables are x, y, and z. The exponents of these variables are 1, 2, and 3. We had these together to get 6. 6 is the degree of the term . Since there is only one term, the degree of the polynomial will be 6 also.

 

Example 6

Identify the degree of each term and the degree of the polynomial: 9x 6 y 5 - 7x 4 y 3 + 3x 3 y 4 + 17x - 4

This polynomial has five terms. To find the degree of each term, we add the exponents of the variables. Let's take it one term at a time.

The degree of the first term will be 11 (we add the exponents of the variables 5+6=11)

The degree of the second term will be 7 (we add the exponents of the variables 4+3=7)

The degree of the third term will be 7 (we add the exponents of the variables 3+4=7)

The degree of the fourth term will be 1 (the only exponent in this term is 1)

The degree of the fifth term will be 0 (this term has no variables so its degree is 0)

The degree of the polynomial will be 11 since 11 is the highest degree of the terms.

 

Example 7

Identify the degree of each term and the degree of the polynomial: 8xy + 9x 2 y 2 + 2x 3 y 3

This polynomial has three terms. To find the degree of each term, we add the exponents of the variables. Let's take it one term at a time.

The degree of the first term will be 2 (we add the exponents of the variables 1+1=2)

The degree of the second term will be 4 (we add the exponents of the variables 2+2=4)

The degree of the third term will be 6 (we add the exponents of the variables 3+3=6)

The degree of the polynomial will be 6 since 6 is the highest degree of the terms.

 

To put a polynomial in Descending Order we arrange the terms in order from the highest exponent down to the lowest exponent. We are only concerned with the first variable if the polynomial has more than one variable.

 

Example 8

Put the polynomial in descending order for x: 3x + 2x 2 - 4

We need to re-arrange the terms from the highest exponent to the lowest. 2 is the highest exponent so we put 2x 2 first. The next highest exponent is 1 so we put the 3x next. The -4 will go last: 2x 2 + 3x - 4

Example 9

Put the polynomial in descending order for x: 6x 2 y - 4x 3 y 4 - 3x y 2

We need to re-arrange the terms from the highest exponent to the lowest. We have two variables, but we are only concerned about the x. 3 is the highest exponent of x so we put - 4x 3 y 4 first. The next highest exponent of x is 2 so we put the 6x 2 y next. The - 3x y 2 xy will go last: - 4x 3 y 4 + 6x 2 y - 3x y 2

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