In problems 1-3, expand and simplify.

1. − 3(4 1)x 2. ( )5 3 2x x x x − − −

3. ( )22 2 2 ( 2)x x− − − − −

#4- 11 Factor completely over the complex numbers.

4. 216 48 27x x− + 5.

280 160 100− −x x

6) 8x3 – 27 7) x4 + 21x2 – 100

8) 3 3 1−a b 9)

2 24 4 3x xy y− −

10) 2 5 2 4(4 3) 12(4 3)x x− + − 11)

3 26 9 10 15x x x− + −

Trig HTrig HTrig HTrig H Name:Name:Name:Name:

R3, 4.1, 4.3 ReviewR3, 4.1, 4.3 ReviewR3, 4.1, 4.3 ReviewR3, 4.1, 4.3 Review

12. Use the graph below to answer the questions that follow.

List the real zeros:

List the turning points:

Use limits to describe the end behavior of the graph:

(13-14) Use limits to describe the end behavior of each (do NOT use your graphing calc!)

13. 2( ) 3 7 2f x x x= − − + 14. 5 24 3 18y x x= − + −

15 - 16 Divide, using any method of your choice:

15. 5 3 22 1 8 4 3 10 6x x x x x+ − + − +

16. (3x3 + 5x – 2) i (x+1)-1

17. If P(x) = -3x3 + 5x2 – 12x – 13, use the remainder theorem to find P(-6) and P(2).

18. Circle the numbers that are zeros of the polynomial: P(x) = (x – 4)(x + 7)3(x2 + 9)(x2 – 2x + 2)

Zeros: 4, 3, 3 , 1 , 1 3i i i+ +

19. Given the polynomial P(x) = 6x3 + 5x2 − 3x − 2; with a factor of (3x – 2), find all other factors.

20. Without a calculator, find all the zeros of the polynomial: x4 + 2x3 – 9x2 – 2x + 8

21. Find all the zeros of p(x) given that one of its zeros is 2-i ; 4 3 2( ) 6 15 18 10p x x x x x= − + − +

22. P(x) = 6x4 – 11x3 + 19x2 – 99x – 315 (calc okay)

a. Find all zeroes of the polynomial

b. Write the polynomial as a product of linear factors!

23. Sketch = − + −3 2( ) 2( 4) ( 5)P x x x using the criteria below. What is the degree of the polynomial? Describe the end behavior. What are the zeros? Be sure to discuss multiplicity. Find the y-intercept: