1. Identify Equations That Are Polynomials

Unit 1: Polynomials

Review

Topics Covered:

1. Identify equations that are polynomials

2. Identify graphs of polynomials

·  ie. be able to tell by inspection a cubic from a quartic.

·  figure out how many roots a polynomial could have

·  identify absolute/relative maximums and minimums

·  determine the domain and range

3. Write the equation of a polynomial given its roots and a point

·  in a written list

·  reading this information off of a graph

4. Graph a polynomial given its roots

·  we should include the y-intercept on our graph

5. Solve a cubic by factoring, where x is a common factor

6. The Remainder Theorem

·  If a polynomial is divided by x - k then the remainder is:

7. The Factor Theorem

·  If x – k is a factor then the remainder is:

8. The Factor Property

·  How do you find test points?

9. Factor a polynomial

·  Long Division and Synthtic Division

·  then graph it

·  list the roots if you are asked to solve

Homework:

p. 28

p. 70

p. 78

Examples:

1.  Which of the following are polynomials?

a) b) c)

d) e)

2.  How many roots could have?

3.  How many different roots does have?

4.  Find the equation of the polynomial with zeros 2, 2, -1, 3 and with y-intercept 10.

5.  Sketch the graph of a polynomial of degree 5 with a 0 and roots at -5, -2, -2, 3, 6

6.  If is divided by , the remainder is 16. What is the remainder if it is divided by ?

7.  Divide by

8.  The product of 3 integers is . The first number is 4 less than the second and the third number is 3 more than the second. Determine the 3 numbers algebraically.

9.  Factor and graph the polynomial,