POLYNOMIALS AND RATIONAL EXPRESSIONS
Polynomial in standard form:
where n ≥ 0 is an integer and
are constants
called the coefficients.
A polynomial with one term is called a monomial:
where k is a whole number. The monomials that form a poly-
nomial are called terms.
For a polynomial
Polynomial? Yes/No Coefficients Degree
Adding and Subtracting Polynomials
Polynomials are added and subtracted by combining the
mono -
mials that may differ only by coefficients.
Example: Perform the indicated operations
Multiplying Polynomials
Two polynomials are multiplied by using the Properties of Real
Numbers and Laws of Exponents .
Example:
Find the product:
Special Products
Evaluate: (2a + 3)(2a − 3) =
Evaluate: 
Evaluate: 
Factoring is the process of expressing a polynomial as a
prod-
uct of two or more nontrivial polynomials.
Example: 
A polynomial is called prime or irreducible if it cannot
be
written as a product of two nontrivial polynomials.
Factoring out the common factor
Factor the following:
Factoring by grouping
Factor: 
Factor: 
Factor: 
Factor: 
Factor: 
A rational expression is a quotient
of
two polynomials,
Example:
Simplify Rational Expressions
Multiplication and Division of Rational Expressions
Addition and Subtraction of Rational Expressions
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