Practice Page
Directions: Answer these questions pertaining to factoring polynomials. Choose the best answer.

1.
The area of a larger rectangle is 6a(4a + 3) and the area of a smaller rectangle is 5(4a + 3). What is the difference of the areas, in factored form?
rectangles
       Choose:
 
(4a + 3)(6a - 5)
(4a + 3) - (6a - 5)
  (4a + 3)(6a + 5) (4a + 3) + (6a - 5)

 

 

2.
Kyle calls to tell you that he has found the correct factors to the homework problem dealing with the difference of two squares. Which of the following could he possibly tell you is his answer? (Assume his answer is correct!)
Kyle2
Choose:
(2a + b)(a - 2b)
(2b - 5)(b - 5)
(a - 5)(a - 5) (2a + 3b)(2a - 3b)

 

 

3.
Given:  2x3 - 10x2 + 8x   and   2x(x2 - 5x + 4).
Which of the following statements is NOT true regarding these polynomial expressions?
       Choose:
 
(x - 4) is a factor of both expressions.
  x2 + 5x + 4 is a factor of both expressions.
  2x is a factor of both expressions
  (x - 1) is a factor of both expressions.

 

 

4.
The diagram at the right shows two squares. What is the area of the orange section, expressed in factored form?
       Choose:
 
(a - b)(a - b)
(a + b)(a + b)
 
(a - b)(a + b)
(a2 + b2 )

 

 

5.
A ceremonial red carpet is rectangular in shape and covers 2x2 + 11x + 12 square feet. If the width of the carpet is (x + 4) feet, express the length, in feet.
redcarpett
       Choose:
 
x + 3
2x + 3
3x + 3
4x + 3

 

 

6.
You are playing a game of "Deal-A-Math" and you draw the card shown below. What is the correct response?
dealmath
Choose:
x - 4
 x + 4
x - 2
 x + 2

 

 

7.
a. A teacher sees the following factoring on a student's paper. Is this factoring correct?
4(x - 3)2 - 8(x - 3) = 4(x - 3)[(x - 3) - 2] = 4(x - 3)(x - 5)
Choose:
YES
NO

b. What is the value of 4(x - 3)2 - 8(x - 3) - 4(x - 3)(x - 5)?
Choose:
1
0
-12x + 44
24x + 48

 

 

8.
Which of the following expressions cannot be used to express the area of the blue shaded regions of this rectangle?
bluefactorrectangle
      Choose:
 
x(x + y) - y(x + y)
x2 - y2
  (x - y)(x - y) (x - y)(x + y)

 

 

9.
You have the final question in the Annual Math Tournament that will win the trophy for your team. The question asks you to fill in the blanks in the following statement, so to create an equivalent statement:
Choose:
m3p; 9m
 m3; 3
m3; 3m
 m3; 9

 

 

10.
Which of the following expressions represents the area of the circle shown at the right.
      Choose:
 
(x2 + 4x+ 4)π sq.in.
(x2 + 4)π sq.in.
  (x2 - 4)π sq.in. (2x + 4)π sq.in.



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