# 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 quotientof
two polynomials,

Example:

** Simplify Rational Expressions**

**Multiplication and Division of Rational Expressions**

**Addition and Subtraction of Rational Expressions**

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