Directions: Answer these questions pertaining to factoring by grouping. In the factoring questions, only completely factored answers are deemed as correct.

1.
Factor completely:  3a3 + 12a2 + a + 4

Choose:
 (a + 12)(3a2 + 1) (a + 4)(3a2 + 2) (a + 4)(3a2 + 1) (a + 4)(3a2 + 4)

2.
Factor completely:   2x3 + 6x2 - 4x - 12

Choose:
 2(x + 3)(x2 - 2) (2x + 3)(x2 - 2) (2x + 6)(x2 - 2) 2(x + 3)(x2 + 2)

3.
Factor completely:   3x2 + xy2 - 3xy - y3

Choose:
 (3x + y2)(x + y) 3xy2(x - y)(x - 1) (3x - y2)(x - y) (3x + y2)(x - y)

4.
Factor completely:   m2x2 + m2b - 2nx2 - 2nb

Choose:
 (x2 - b)(m2 - 2n) (x2 - b)(m - n) (x2 + b)(m2 - 2n) (x2 + b)(m - n)

5.
Factor completely:  3n3 + 2n2 - 3n - 2

Choose:
 (n2 + 1)(3n + 2) (n + 1)(n - 1)(3n + 2) (n2 - 1)(3n + 2) (n + 1)(n - 1)(3n - 2)

6.
When a2(a + b)4 - b2(a + b)4 is expressed as
(a + b)m(a - b), what is the value of m?

Choose:
 8 6 5 4

7.
a) Which of the following expressions is equivalent to 5x3 - 6x2y - 45xy2 + 54y3
Choose:
 x2(5x - 6y) + 9y2(5x + 6y) x2(5x - 6y) + 9y2(5x - 6y) x2(5x - 6y) - 9y2(5x + 6y) x2(5x - 6y) - 9y2(5x - 6y)

b)
Which of the following expressions is NOT a factor of 5x3 - 6x2y - 45xy2 + 54y3

Choose:
 5x - 6y x2 + 9y2 x - 3y x + 3y

8.
Factor by grouping: 10x3 - 2x2y2 - 5xy + y3
Choose:
 (2x2 - y)(5x - y2) (2x - y2)(5x2 - y) (5x2 - y)(2x - y2) (2x2 - y)(5x - 2y2)

9.
Factor by grouping:   2ax2 + 3axy - 2nxy - 3ny2

Choose:
 (ax - ny)(2x - 3y) (ax + ny)(2x + 3) (2x + 3y)(ax + ny) (2x + 3y)(ax - ny)

10.
Factor completely:  x5 - 3x3 - 5x2 + 15

Choose:
 (x2 - 3)(x3 - 5) (x2 - 3)(x3 + 5) (x3 - 3)(x2 - 5) (x3 - 3)(x2 + 5)

 11. Which expressions are equivalent to 243x4 - 216x2 + 48 ? (Check all that apply, and hit SUBMIT!) 3(9x2 + 4)(9x2 - 4) 3(9x2 - 4)(9x2 - 4) 3(9x2 + 4)(9x2 + 4) 3(81x2 + 4)(81x2 - 4) 3(81x4 - 72x2 + 16) 3(3x2 - 4)(3x2 - 4) 3(3x - 2)2(3x + 2)2