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Systems of Equations
Adding and Subtracting Rational Expressions with Different Denominators
Graphing Linear Equations
Raising an Exponential Expression to a Power
Horizontal Line Test
Quadratic Equations
Mixed Numbers and Improper Fractions
Solving Quadratic Equations by Completing the Square
Solving Exponential Equations
Adding and Subtracting Polynomials
Factorizing simple expressions
Identifying Prime and Composite Numbers
Solving Linear Systems of Equations by Graphing
Complex Conjugates
Graphing Compound Inequalities
Simplified Form of a Square Root
Solving Quadratic Equations Using the Square Root Property
Multiplication Property of Radicals
Determining if a Function has an Inverse
Scientific Notation
Degree of a Polynomial
Factoring Polynomials by Grouping
Solving Linear Systems of Equations
Exponential Functions
Factoring Trinomials by Grouping
The Slope of a Line
Simplifying Complex Fractions That Contain Addition or Subtraction
Solving Absolute Value Equations
Solving Right Triangles
Solving Rational Inequalities with a Sign Graph
Domain and Range of a Function
Multiplying Polynomials
Slope of a Line
Inequalities
Multiplying Rational Expressions
Percent of Change
Equations Involving Fractions or Decimals
Simplifying Expressions Containing only Monomials
Solving Inequalities
Quadratic Equations with Imaginary Solutions
Reducing Fractions to Lowest Terms
Prime and Composite Numbers
Dividing with Exponents
Dividing Rational Expressions
Equivalent Fractions
Graphing Quadratic Functions
Polynomials
Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
Factoring Polynomials Completely
Using Slopes to Graph Lines
Fractions, Decimals and Percents
Solving Systems of Equations by Substitution
Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Conjugates
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Formulas
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Roots
Adding and Subtracting Polynomials
The Rectangular Coordinate System
Polar Form of a Complex Number
Exponents and Order of Operations
Graphing Horizontal and Vertical Lines
Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
 
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Polynomials

Recall that a monomial is a number, a variable, or a product of numbers andvariables. A polynomial is a monomial or a sum of monomials. The exponents of the variables of a polynomial must be positive. A binomial isthe sum of two monomials, and a trinomial is the sum of three monomials. The degree of a monomial is the sum of the exponents of its variables. To find the degree of a polynomial, you must find the degree of each term. The greatest degree of any term is the degree of the polynomial. The terms of a polynomial are usually arranged so that the powers of one variable are in ascending or descending order.

Examples

Consider the expression .

A Is the expression a polynomial and if so is it a monomial, binomial, or trinomial?

The expression is the sum of three monomials, therefore it is a polynomial. Since there are three monomials, the polynomial is a trinomial.

B What is the degree of the polynomial?

The degree of is 2, the degree of 5 is 0, and the degree of 7x is 1. The greatest degree is 2, so the degree of the polynomial is 2.

C Arrange the terms of the polynomial so thatthe powers of x are in descending order.

 

Adding and Subtracting Polynomials

To add polynomials, you can group like terms and then find their sum, or youcan write them in column form and then add. To subtract a polynomial, add its additive inverse, which is the opposite of each term in the polynomial.

Examples

Find each sum or difference.

A

Arrange like terms in column form and add. Follow the rules for adding signed numbers.

B (12x + 7y ) - (- x + 2y )

Find the additive inverse of - x + 2y. Then group the like terms and add. The additive inverse of - x + 2y is x - 2y.

(12x + 7y ) - (- x + 2y )

= (12x + 7y ) + (+ x - 2y )

= (12x + x) + (7y - 2y)

= 13x + 5y

 

Multiplying a Polynomial by a Monomial

Use the distributive property to multiply a polynomial by a monomial. Youmay find it easier to multiply a polynomial by a monomial if you combine alllike terms in the polynomial before you multiply.

Examples

Find

Solution

Combine like terms in the polynomial and then multiply using the distributive property.

 

Multiplying Polynomials

Use the distributive property to multiply polynomials. If you are multiplying two binomials, you can use a shortcut called the FOIL method.

To multiply two binomials, find the sum of the products of

FOIL Method for Multiplying Two Binomials F the First terms

O the Outer terms

I the Inner terms

L the Last terms

 

Example

Find (2x + 3)(4x - 1).

 
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