 1. What are the Properties of Exponents?  2. How do we convert between exponential and radical form?  3. How do we add, subtract, and multiply polynomials?

Properties of Exponents & Performing Operations with Polynomials (Adding, Subtracting, & Multiplying)

What are  Mono- is a prefix meaning “one”  Bi- is a prefix meaning “two”  Tri- is a prefix meaning “three”  Poly- is a prefix meaning “many”  -nomial is a suffix meaning “terms”  Polynomial = Many Terms Polynomials?

How do we work with  We can perform operations with polynomials (addition, subtraction, multiplication, and division). (Division is taught in Math III).  When we write polynomials, the standard is to write in descending order of the exponents.  The degree of a polynomial is the highest exponent or sum of the exponents if there are multiple variables in the same term. Polynomials?

 1. 5p 2 – 3  2. a 3 – 2a 2  3. 3 – 6n 5 – 8n 4  x 4 y 3 + 6y 3 + 4x 4 y 4  A. trinomial degree 8  B. binomial degree 2  C. trinomial degree 5  D. binomial degree 3

Combining Like Terms

Adding the Opposite.

ADDING POLYNOMIALS  (5p 2 -3) + (2p 2 – 3p 3 )  Identify like terms and combine them. 5p 2 + 2p 2 = 7p 2  Write in descending order of the exponents.  -3p 3 + 7p 2 -3 SUBTRACTING POLYNOMIALS  (a 3 – 2a 2 ) – (3a 2 – 4a 3 )  Add the opposite, so… (a 3 – 2a 2 ) + (-3a 2 + 4a 3 )  Combine like terms… a 3 + 4a 3 = 5a 3 -2a a 2 = -5a 2  5a 3 – 5a 2

 (-7x – 2x) + (10x 4 + 7x + 5x 5 )  Reorder  -7x 5 + 5x 5 +10x 4 – 2x + 7x + 14  Combine like terms  -2x x 4 + 5x + 14

 (8n – 3n n 2 ) – (3n n 4 – 7)  8n – 3n n n n  -3n n n n 2 + 8n + 7  Combine like terms  -14n 4 + 7n 2 + 8n + 7

 When multiplying, multiply the constants, then the variables.  Remember to use the laws of exponents (when multiplying you add the exponents).  Ex: 2x 2 * 5x 3 = 10x 5

 To multiply a monomial and a polynomial, you simply distribute.  Ex: 2x 2 (3x 3 – 4x 2 + x – 5) 6x 5 – 8x 4 + 2x 3 – 10x 2

 FOIL – multiply first, outside, inside, then last (basically distribute)  Box it – draw a box, put the numbers in, multiply and combine like terms.  Examples:  1. (x + 2) (x + 5)  2. (3x + 10) (2x – 5)

 1) Distribute 2) Line up your like terms 3) Add  Or… Box it Ex: 1. (x + 2) (x 2 + 5x + 6) 2. (x 2 – 2x + 1) (x 2 + 5x + 6) 3. (2x 2 – 3x + 4) (x 4 + 2x 3 – 4x – 3)

On Notebook Paper:  Classwork: Odd Problems  Homework: Even Problems

 On a half piece of notebook paper, answer the following:  1. When do you add the exponents?  2. When do you subtract the exponents?  3. When do you multiply the exponents?  4. How do you get 1 when using exponents?  5. If something is raised to the 1/3 power, what is the root?