ELEMENTARY ALGEBRA REVIEW FOR TEST 4

Test also includes review problems from earlier sections so study test reviews 1, 2, and 3 also.

1. Factor completely : a² – b²
2. Factor completely: a² + b²
3. Factor completely: a² – 2ab + b²
4. Factor completely: a² + 2ab + b²
5. Factor completely: a³ – b³
6. Factor completely: a³ + b³
7. Factor completely: 9ab³ – 6a²b²
8. Factor completely: 10a³ + 6a²b – 2a
9. Factor completely: 21x³y²z⁴ – 28x⁵y³
10. Factor completely: 12x² – 3xy – 8x + 2y
11. Factor completely: 5x² + 5xy – x – y
12. Factor completely: x² – 9x + 20
13. Factor completely: x² – 15x – 14
14. Factor completely: 2y² + 4y – 48
15. Factor completely: 2x² + 7x + 6
16. Factor completely: 6y² + 7y – 20
17. Factor completely: 2x³ – 7x² – 30x
18. Factor completely: 3x² – 16x + 5
19. Factor completely: 9a² + 42a + 49
20. Factor completely: y² – 12y + 36
21. Factor completely: 25x² – 10x + 1
22. Factor completely: 2x³ – 18x
23. Factor completely: 49a² – 81b²
24. Factor completely: 25x² + 36y²
25. Factor completely: 64w³ – 1
26. Factor completely: 8a³ + 125c³
27. Factor completely: 2x³ – 54

28. Review solving equations with denominators , graphing , slope of a line , word problems
that can be solved by a system of equations , word problems involving area and
perimeter, and solving formulas for one of the variables . (Pay particular attention to the
types of problems I have mentioned that people had problems with on earlier tests in
the announcements section of Blackboard.)

ANSWERS:

1. (a – b)(a + b) [NOTE: Know this formula , and use it for factoring a difference of two
squares .]
2. Prime (Not Factorable) [NOTE: Know this formula. A sum of two squares is not
factorable unless it has a common factor. If it has a common factor, factor it out.]
3. (a – b)² [NOTE: Know this formula, and use it for factoring a perfect square trinomial
with a negative middle term .]
4. (a + b)² [NOTE: Know this formula, and use it for factoring a perfect square trinomial
with a positive middle term.]
5. (a – b)(a² + ab + b²) [NOTE: Know this formula, and use it for factoring a difference of
two cubes . If you have factored out common factors first, the trinomial part of the
answer will not factor further.]

6. (a + b)(a² – ab + b²) [NOTE: Know this formula, and use it for factoring a sum of two
cubes. If you have factored out common factors first, the trinomial part of the answer will not
factor further.]

7. 3ab²(3b – 2a)
8. 2a(5a² + 3ab – 1)
9. 7x³y²(3z⁴ – 4x²y)

10. (4x – y)(3x – 2)
11. (x + y)(5x – 1)
12. (x – 4)(x – 5)
13. Prime (Not Factorable) [NOTE: (x – 14)(x – 1) = x² – 15x + 14, not x² – 15x – 14]
14. 2(y + 6)(y – 4)
15. (2x + 3)(x + 2)
16. (2y + 5)(3y – 4)
17. x(2x + 5)(x – 6)
18. (3x – 1)(x – 5)
19. (3a + 7)²
20. (y – 6)²
21. (5x – 1)²
22. 2x(x + 3)(x – 3)
23. (7a + 9b)(7a – 9b)

10. (4x – y)(3x – 2)
11. (x + y)(5x – 1)
12. (x – 4)(x – 5)
13. Prime (Not Factorable) [NOTE: (x – 14)(x – 1) = x² – 15x + 14, not x² – 15x – 14]
14. 2(y + 6)(y – 4)
15. (2x + 3)(x + 2)
16. (2y + 5)(3y – 4)
17. x(2x + 5)(x – 6)
18. (3x – 1)(x – 5)
19. (3a + 7)²
20. (y – 6)²
21. (5x – 1)²
22. 2x(x + 3)(x – 3)
23. (7a + 9b)(7a – 9b)

24. Prime (Not Factorable) - Sum of Squares [NOTE: If you got a different answer ,
carefully multiply it back together to see that it is not equal to the original problem.]
25. (4w – 1)(16w² + 4w + 1)
26. (2a + 5c)(4a² – 10ac + 25c²)
27. 2(x – 3)(x² + 3x + 9)