Algebra 1 Review Polynomials & Factoring

Pre-Calculus—Prerequisite Knowledge &Skills
III.Polynomials

A.Exponents
The expression bn is called a power or an exponential expression.
This is read “b to the nth power”
The b is the base, and the small raised symbol n is called the exponent.

The exponent indicates the number of times the base occurs as a factor.

Examples—Express each of the following using exponents.
a. 5 x 5 x 5 x 5 x 5 x 5 x 5 =
b. 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 =
c. 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 =

The powers of a number b can be written in factored form or in exponential form.

Factored FormExponential Form
First power of bbb (= b1)“b to the first power” (we normally do not write the 1 for a first power—it is just understood) Second power of b b x bb2“b to the second power”,

or “b squared”

Third power of b b x b x bb3“b to the third power”,
or “b cubed”

Fourth power of b b x b x b x bb4“b to the fourth power”

Example—Evaluate x3 if x = – 2

Example—Evaluate if x = 2

B.Adding and Subtracting Polynomials

Examples of Monomials7h–8x2y

A monomial is an expression that is either a number, a variable, or is a product of a numeral and one or more variables. Monomials (such as 7) that consist of only a number with no variables are called a constant monomial or, more simply, a constant.

A sum of monomials is called a polynomial.

A polynomial that consists of the sum of two monomials is called a binomial.
Binomials: 4x – 3 –7a2 + 5b
A polynomial that consists of the sum of three monomials is called a trinomial.
Trinomials:7x2 – 3x + 175b2 + 3ab – a2
Each of the monomials added to form a polynomial is a term of the polynomial.
A monomial is a polynomial with one term.

The number in front of...