1. which of the following is the factored form of the expression: 3x2 – 4x?

a. x(3x - 4)
b. x(3 – 4x)
c. (3x -1) (x -1)
d. (3x +1)(x -1)

2. which is a completely factored form of the expression: x2 + 21x +20 ?

a. (x + 5)(x + 4)
b. (x + 10)(x + 2)
c. (x + 20)(x + 1)
d. (x + 21)(x - 1)

3. which expression is factored form of 4x2 -9?

a. 2(x - 3)2
b. (x - 3)2
c. 2(x + 3)(x - 3)
d. (2x + 3)(2x - 3)

4. below are factored forms of the expression: 12x3 – 36x2 . which expression has the greatest common factor as the first term?

a. 3x (4x2 – 12x)
b. 4x2(3x -9
c. 12x2(x – 3)
d. 12x(x2 - 3x)
5. adele’s lawn has an area of (x2 -5x -6) square feet and a length of (x + 1) feet. what is the width of the lawn in feet?

a. (x -6)
b. (x +6)
c. (x2 -4x -5)
d. (x2 -6x -7)

6. the expression below represents the area, in square meters, of a rectangle:
x2 + 5x -24
which of the following pairs of expressions could represent the length and width, in meters, of the rectangle?

a. (x – 3) and (x + 8)
b. (x – 4) and (x + 6)
c. (x – 6) and (x + 4)
d. (x – 8) and (x + 3)

7. what is the complete factorization of 32 – 8z2?

a. -8(2 + z)(2 –z)
b. 8(2 + z)(2 – z)
c. -8(2 + z)2
d. 8(2 – z)2

8. what is the greatest common factor of: 12x2 , 24x2y2 , and 46xy?

a. 4x
b. 3x
c. 6x
d. 2x
9. which expression is equivalent to: 2x2 -3x -35?

a. (2x + 7)(x - 5)
b. (2x - 7) (x + 5)
c. (2x - 5)(x + 7)
d. (2x + 5)(x - 7)

10. what are the factors of 81x2 + 36x + 4?

a. (9x + 2)(x +2)
b. (9x +2)(9x +2)
c. (9x -2)(9x -2)
d. (9x +2)(9x -2)

11. the top of a rectangular table has an area of: 18x2+ 69x +60.
the width of the table is 3x + 4. what is the length of the table?
(show proof by multiplying – show your work)

12. simplify: (x2 +2x)(5x -3)
a. 11x2 -3
b. 6x3 -6x
c. 5x3 + 7x2 – 6x
d. 5x3 – 13x2 -6x

13. factor by grouping: 30g5 +24g3h – 35g2h2 - 28h3 show your work!

14. which is the correct way to factor the polynomial : x2 -16?

a. (x -4)(x -4)
b. (x -4)(x +4)
c. (x +4)(x -2)(x +2)
d. not factorable

15. the area of a square painting is: 81p2 + 90p +25. what is the length of one side? prove by multiplication – show your work.