Algebra 1B Name:__________________________

Unit 6 Classwork/Homework

Unit 6 Test Review WS

Directions: Complete the following problems, showing all work. Write your final answer(s) on this worksheet. When

finished, check your answers with the answer key provided. We will not be going over this worksheet, so you must see Mrs.

BEch before class if you have any questions! This counts as a homework assignment, and completion of the entire assignment

makes you eligible for 2nd chance learning on the Unit 6 Test if you score below a 70%.

Directions: Complete the following concept questions

1) What is the first step to every factoring problem? ____________________________________________________________________________________

2) If a problem cannot be factored, what is the answer?_________________________________________________________________________________

3) What is the difference between factoring and solving?________________________________________________________________________________

4) Explain why 𝑥2 + 36 is not a DOTS problem. __________________________________________________________________________________________

5) What is the name of the property used to solve by factoring?________________________________________________________________________

Directions: Factor each polynomial. Each of these polynomials will use only one factoring strategy. (2 are prime)

6) 𝑥2 − 16 7) 40 + 13𝑥 + 𝑥2 8) 𝑥2 − 16𝑥 + 64 6)__________________________

7)__________________________

8)__________________________

9) 3𝑥2 + 17𝑥 + 10 10) 4𝑥2 + 16𝑥 11) 25 − 9𝑥2 9)__________________________

10)_________________________

11)_________________________

12) 𝑥2(𝑦 − 7) + 3(𝑦 − 7) 13) 𝑥2 − 6𝑥 + 10 14) 10𝑥2 − 27𝑥 + 5 12)_________________________

13)_________________________

14)_________________________

15) 12𝑥3 + 15𝑥2 − 8𝑥 − 10 16) −8𝑥2 + 4𝑥 17) 4 + 𝑥2 15)_________________________

16)_________________________

17)_________________________

Directions: Factor the following polynomials completely. Show your work. None are prime.

18) 8𝑥3 − 18𝑥 19) 2𝑥2 − 20𝑥 + 32 20) −3𝑥2 + 15𝑥 + 42 18)_________________________

19)_________________________

20)_________________________

21) 4𝑥3 + 8𝑥2 + 3𝑥 22) 𝑥3 + 3𝑥2 − 100𝑥 − 300 23) 4𝑥3𝑎 − 12𝑥2𝑎 − 16𝑎𝑥 21)_________________________

22)_________________________

23)_________________________

Directions: Solve each equation by factoring. Show your work. None are prime.

24) 36𝑥2 − 1 = 0 25) 2𝑥2 + 22𝑥 = −56 26) −8𝑥2 + 48𝑥 = 0 24)______________

25)______________

26)______________

27) 3𝑥2 − 17𝑥 + 7 = 2𝑥 + 1 28) 4𝑥3 + 12𝑥2 − 𝑥 = 3 29) −2𝑥2 + 95 = −3 27)______________

28)______________

29)______________

Directions: Define your variables, set up an equation, then solve. Label your final answers.

30) The sum of a positive number and its square is 56. Find the number. 30) The number is_______.

31) The length of a rectangle is 5 inches more than the width. The area of the rectangle 31) length = ________

is 66 𝑖𝑛2. Find the dimensions of the rectangle. width = ________

32) The product of two consecutive negative even integers is 360. Find the integers. 32) The integers are

_________ and __________.

33) Eight less than the square of a positive number is the same as 2 times the number. Find the number.

33) The number is ______.