Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

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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.


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.


Find each sum or difference.


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.




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



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