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Rational Expressions and Their Simplification
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Simplifying Algebraic Expressions
Rational Expressions and Functio
Rational Expressions and Functions
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Rational Expressions Worksheet
Adding and Subtracting Rational Expressions
Rational Expressions
Multiplying and Dividing Rational Expressions
Dividing Fractions, Mixed Numbers, and Rational Expressions
Multiplying and Dividing Rational Expressions
Multiplying and Dividing Rational Expressions
Simplifying Rational Expressions
Complex Rational Expressions
Rational Expressions and Equations
Integration of Polynomial Rational Expressions
Algebraic Expressions
Radical Expressions & Radical Functions
Rational Class and Expression Evaluator
Adding and Subtracting Rational Expressions
Rational Expressions
Radical Expressions
Multiplying Rational Expressions
Rational Expressions and Common Denominators
rational expressions
Polynomial Expressions
Rational Functions, and Multiplying and Dividing Rational Expressions
Simplifying Radical Expressions
Adding and Subtracting Rational Expressions
Rational Expressions and Equations
Rational Expressions
RATIONAL EXPRESSIONS II
Simplifying Expressions
Quadratic Expressions,Equations and Functions
RATIONAL EXPRESSIONS
Absolute Value and Radical Expressions,Equations and Functions
Rational Expressions & Functions

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Polynomial Expressions

A polynomial is an expression which involves various powers of a variable. Some examples are:
and 5. The general form for a polynomial is:

Here the coefficients (a's) can be any real number. The number n, which is an integer, is known as the degree of the polynomial.

EX. is a polynomial of degree 3, with leading coefficient 5, and constant term -2.
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Classifying Polynomials

Polynomials can be classified based on the degree (largest power), or based on the number of terms.

1 term = monomial
2 terms = binomial
3 terms = trinomial
and so on…

EX. is a binomial of degree 5.

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Basic Operations on Polynomials

Just like with numbers, we often want to add, subtract, multiply and divide polynomials.

Addition

Adding polynomials is simply collecting like terms

EX.

Subtraction:

To subtract two polynomials, you simply use the distributive law, then collect like terms.

EX.

Notice you distribute the minus sign.

Multiplication:

While adding and subtracting were fairly easy, multiply two polynomials can quickly become a headache. To multiply you must repeatedly apply the distributive law, then collect like terms.

EX.

Notice that the distributive law was applied four times to complete that single multiplication

Division:
Division will be covered when we go into Rational Expressions. Notice that if you add, subtract, or multiply two polynomials, you end up with a polynomial again. This is not always true for division, and this is the reason we postpone this topic.
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FOIL

There is a special case for multiplying polynomials, which occurs when you multiply a binomial times a binomial. In this case it is easier to use FOIL.

EX.