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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

Factoring using a formula

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

Compound Fractions

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