Definition: Repeated multiplication
a is called the base
n is called the exp onent or power
Examples
Note: Parentheses are important.
Powers of negative base
Exponent Rules :
Example
Example
Example
Example
Example
Concept
Concept
Divide both sides by 
Examples
Example
Example
Example
Homework:
Simplify by writing out the repeated multiplications.
Simplify by using an exponent rule.
Simplify using exponent rules.
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4.2 Polynomials
| Power Term Form |
|
|
| One Variable |
|
Two Variables |
 |
or |
 |
Polynomials are made by summing power terms.
Example
Standard Form for Polynomials
Adding Polynomials
Combine like terms
Example
(3x + 5)+ (4x - 7)
| Horizontal |
Vertical |
 |
 |
Example
Subtracting Polynomials
Subtracting is adding the opposite.
Examples
Examples
Homework: Perform the operations .
4.3 Multiplying Polynomials
Multiply Terms
Example
Steps
1. Multiply coefficients .
2. Add exponents of the same variable.
When we multiply we distribute and multiply terms.
Distribution Property
Examples
Multiplying Binomials
FOIL Distribution
Examples
Note: Always combine like terms when possible.
Example
Extending the distribution rule
Distribute each term in first polynomial into the second polynomial.
Example
Concept for multiplying polynomials
1. Distribute
2. Multiply terms
3. If necessary, combine like terms (add or subtract).
Homework:
4.4 Dividing Polynomials
Dividing Terms
Example
Concept
1. Divide or reduce the coefficients .
2. Subtract the exponents (powers) of the same variable.
Examples
Dividing Polynomials by a Monomial
1. Rewrite using the denominator under each term.
2. Divide the terms.
Examples
Dividing Polynomials by a Binomial
We will use Long Division to divide.
Concept
1. Divide the highest degree term of divisor into highest degree term of
dividend.
2. Multiply the Quotient term from step 1 onto the divisor.
3. Subtract the product in step 2 from the dividend.
4. Repeat steps 1, 2, and 3 until degree of remainder is less than degree of
divisor.
Example
Example
Example
We can divide by more terms in the divisor.
Example
Homework: Divide
Use Long Division to divide.
