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 Form Exponential Form

First power of b b b (= 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 b b2 “b to the second power”, or “b squared”

Third power of b b x b x b b3 “b to the third power”, or “b cubed”

Fourth power of b b x b x b x b b4 “b to the fourth power”

Example—Evaluate x3 if x = – 2

Example—Evaluate if x = 2

B. Adding and Subtracting Polynomials

Examples of Monomials 7 h –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 + 17 5b2 + 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