**Get signed by your parents for 5 bonus points on the test!! Ch. 5 Review **Get signed by your parents for 5 bonus points on the test!!

Simplify the expressions. 1. 49 𝑎 3 𝑏 −4 𝑐 7 35 𝑎 5 𝑏 −2 𝑐 −9. 2

What is the end behavior of the function 3. f(x) = 𝑥 7 + 𝑥 5 − 𝑥 3 ?

Perform the indicated operation. 4

Factor the polynomial completely 6. 8𝑥 3 −27 7. 𝑥 4 −7 𝑥 2 −18

8. Find all the real zeros of 𝑓 𝑥 = 𝑥 3 + 𝑥 2 −22𝑥−40 8. Find all the real zeros of 𝑓 𝑥 = 𝑥 3 + 𝑥 2 −22𝑥−40 **Remember, real zeros are the same as x-intercepts.

9. List all x-intercepts, local. maximums, and local minimums of

10. Given the zeros −2𝑖 & 2+ 5 write a polynomial equation in factored form.

11. Factor the expression by grouping. 𝑥 3 +3 𝑥 2 −4𝑥−12

12. Use long division to solve 6 𝑥 4 +7 𝑥 2 +4𝑥−17 ÷( 2𝑥 2 +2𝑥+3)

13. Use synthetic division to find the 13. Use synthetic division to find the solutions of 𝑥 3 −6 𝑥 2 +5𝑥+12 given that 𝑥−3 is a factor.

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions.  State the degree, type, and leading coefficient of the polynomial function. Degree: Type: Leading Coefficient:

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions. What is the max number of turns and max number of x-intercepts the graph can have? Turns: X-intercepts:

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions. Make a table of values for the polynomial function that contains at least 5 values. X Y

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions. What will the end behavior of the graph be?

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions. Graph the function.

14. Use 𝑓 𝑥 =𝑥 (𝑥−3) 2 to answer the following questions. State the domain and range.

ANSWER KEY 7 𝑐 16 5 𝑎 2 𝑏 2 6 𝑛 4 𝑚 2 𝑥 3 +8 𝑥 2 −3𝑥+4 7 𝑐 16 5 𝑎 2 𝑏 2 6 𝑛 4 𝑚 2 f(x) -> -∞ as x -> -∞ and f(x) -> +∞ as x -> +∞ 𝑥 3 +8 𝑥 2 −3𝑥+4 2𝑥 2 −𝑥+8− 4 𝑥−5 (2𝑥−3)(4 𝑥 2 +6𝑥+9)

ANSWER KEY (𝑥 2 +2)(𝑥+3)(𝑥−3) X = -4, -2, 4 x-intercepts: -3, -1, 2 local maximums: (-2, -16.7) and (2, 0) local minimums: (0, 12.4) (𝑥−2𝑖)(𝑥+2𝑖)(𝑥− 2+ 5 )(𝑥− 2− 5 ) (x + 3)(x + 2)(x – 2) 3𝑥 2 −3𝑥+2+ 9𝑥−23 2 𝑥 2 +2𝑥+3

ANSWER KEY X = -1, 3, 4 𝑓 𝑥 = 𝑥 3 −6 𝑥 2 +9x 3, cubic, 1 2 turns; 3 x-intercepts Table f(x) -> -∞ as x -> -∞ and f(x) -> +∞ as x -> +∞ Graph D: all real numbers; R: all real numbers