Practice Page
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)
fm2

 

 

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)
fm8

 

 

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)
fm1

 

 

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

Choose:
(x2 - b)(m2 - 2n) (x2 - b)(m - n)
(x2 + b)(m2 - 2n) (x2 + b)(m - n)
fm7

 

 

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)
fm3

 

 

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
fm10

 

 

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
fm4

 

 

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)
fm6

 

 

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)
fm5

 

 

10.
Factor completely:  x5 - 3x3 - 5x2 + 15   
Choose:
(x2 - 3)(x3 - 5) (x2 - 3)(x3 + 5)
(x3 - 3)(x2 - 5) (x3 - 3)(x2 + 5)
fm9

 

 

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

        

pickguysign

 

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