Pre-Calculus—Prerequisite Knowledge &Skills
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.
First power of 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
“b to the second power”,
or “b squared”
Third power of b b x b x b
“b to the third power”,
or “b cubed”
Fourth power of b
b x b x b x b
“b to the fourth power”
Example—Evaluate x3 if x = – 2
Example—Evaluate if x = 2
Adding and Subtracting Polynomials
Examples of Monomials
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.
4x – 3
–7a2 + 5b
A polynomial that consists of the sum of three monomials is called a trinomial.
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...
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