Algebra 1 Review Polynomials & Factoring
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...
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