Math 3 College Prep Unit 4 Worksheet 7--Review

Name:____________________________________ Date:____________________ Period:______

Find a polynomial function that has the given zeros. 1.

0, -3, and 4

2. 1, -3 and -1

3. -4, √7

4.

−2 3

𝑎𝑛𝑑

2 3

Find the possible polynomial function that is represented by each graph. (The x-intercepts of the curve are provided to the right of the graph for clarification.) 5. ___________________

6. __________________

7. _____________________ (-2, 0)

(-4, 0) (-3, 0)

(-1, 0)

(0, 0)

(0, 0)

(1, 0)

(3, 0)

(6, 0)

(4, 0)

Evaluate the following points on the graph of the polynomial function. (SHOW WORK!!!!) 8. f(x) = x3 + 2x2 – 5x – 6 A. f(0)

B. f(-1)

C. f(-4)

D. f(2)

Sketch the following. Remember to factor first where needed to find the real zeros. SHOW ALL WORK. 9. f(x) = -x2 + 16 10. g(x) = 6x2 – 21x + 9 Factored form: Factored form: Degree

Leading Coefficient

End Behavior solutions sketch

Degree

Leading Coefficient

End Behavior y-intercept

x-intercept sketch

y-intercept

11. h(x) = 2x3 – 6x2 – 56x Factored form: Degree

12. g(x) =- x4 + 10x2 - 9 Factored form: Leading Coefficient

End Behavior zeros

Degree

Leading Coefficient

End Behavior y-intercept

sketch

roots

y-intercept

sketch

Use a graphing calculator to answer the following questions. Round to the hundredths place when necessary.

13. h(x) =-x 3 + x2 +16x+20 Max # of turns # Real roots

14. 𝑓(𝑥)−= −2𝑥 4 + 9𝑥 3 − 2𝑥 2 − 9𝑥 + 4 Max # of turns # Real roots

Rel. Max

Rel. Min

Rel. Max

Rel. Min

# Complex roots

# Imaginary roots

# Complex roots

# Imaginary roots

x-intercept

y-intercept

x-intercept

y-intercept

Increasing Interval(s)

Decreasing Interval(s)

Increasing Interval(s)

Decreasing Interval(s)

Domain

Range

Domain

Range

Expand the following binomials. 15. 𝑓(𝑥) = (2𝑥 − 3)5

16. 𝑓(𝑥) = (𝑥 + 5)4

List the 4th terms for each expanded binomials. 17. 𝑓(𝑥) = (7𝑥 + 2)6

18. 𝑓(𝑥) = (𝑥 − 9)7

Perform the indicated operation. Simplify completely. 19. (𝑥 2 + 3𝑥 − 9) − (−6𝑥 2 − 9 + 𝑥 4 )

20. (−𝑥 7 + 10𝑥 5 + 3𝑥) + (−3𝑥 7 − 20𝑥 4 + 9𝑥)

21. (𝑥 2 + 2𝑥 − 5)(𝑥 − 6)

23.

25.

(12𝑥 3 − 11𝑥 2 + 9𝑥 + 18)(4𝑥 + 3)−1

(4𝑥 3 − 2𝑥 2 − 3) ÷ (2𝑥 2 − 1)

22. (𝑥 + 5)2 (𝑥 − 3)

24.

2𝑥 3 +4𝑥 2 −5 𝑥+3

26. (3𝑥 3 + 4𝑥 + 11) ÷ (𝑥 2 − 3𝑥 + 2)

27. Remainder Theorem. What is the value of f(-3) if 𝑓(𝑥) = 𝑥 3 − 2𝑥 2 + 4𝑥 − 1?

List all possible rational zeros. 29. 𝑓(𝑥) = 12𝑥 3 − 3𝑥 2 − 4𝑥 + 2

28.

Factor Theorem. Is (𝑥 + 2) a factor of 3𝑥 2 + 4𝑥 − 𝑥 4 − 2𝑥 3 − 4)

30. 𝑓(𝑥) = 3𝑥 4 − 7𝑥 3 + 9𝑥 2 − 7 + 48

Use the given information to a) write the polynomial in factored form and b) state all roots. 31. (𝑥) = 2𝑥 3 + 𝑥 2 − 2𝑥 − 1 ; x=1 is a zero. 32. 𝑓(𝑥) = 𝑥 3 − 27𝑥 2 + 207𝑥 − 405; (𝑥 − 9) is a factor.

33. 𝑓(𝑥) = 5𝑥 3 + 29𝑥 2 + 19𝑥 − 5; (−5, 0) is an x-intercept.

34. 𝑓(𝑥) = 4𝑥 3 − 9𝑥 2 + 6𝑥 − 1;

*Test will have one portion that is calculator active and part that is not calculator active. *All questions will require work. *Don’t forget to study your word problem worksheets.

1 4

is a root