Algebra
Quiz: Expand and factor polynomial expressions
Name
Expand the following polynomials. Show all work; BOX answers.
1. ( x  6)( x  1)
2. (5 x  5)(5 x  5)
3. (2 x  3)( x 2  6 x  4)
4. Find the area of a rectangular cake (chocolate with raspberry filling) with length (4x – 3) and
width (3x + 7).
Factor each polynomial given below. Show all work; BOX answers.
5. x 2  12 x  36
6. x 2  15 x  56
7. x 2  9
8. Multiply the first set of polynomials and factor the second polynomial. Write a conclusion relating
multiplying and factoring polynomials:
a) (2 x  1)( x  8)
b) 2 x 2  15 x  8
YOU ARE THE TEACHER. The following student’s work is incorrect. Circle the mistake and explain
what the student should have done.Then expand the polynomial correctly.
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( x  5) 2
9.
x 2  52
x 2  25
2
Choose the letter which best answers the question. Circle your answer.

2
DO YOUR FIGURING HERE

10. Which of the following is equal to 2 y 3 2 y 2  5 y  6 ?
a.
4 y  10 y  12 y
b.
4 y5  10 y 4  12 y 3
c.
4 y 6  10 y 4  6 y 3
d.
y5  7 y 4  4 y3
e.
4 y 4  10 y 4  12 y 3
2
4
3
11. Which of the following is equal to  b  8 b  2  ?
a.
b.
c.
d.
e.
b 2  6b  16
b 2  6b  16
b 2  6b  6
b 2  6b  6
b 2  10b  16
12. Find the product of
a.
b.
c.
d.
e.
 x  5  3x 2  2 x  1 ?
3x3  13x 2  10 x  5
3x3  13x 2  10 x  6
3x3  6 x 2  6 x  6
3x3  13x 2  9 x  5
3 x 3  17 x 2  9 x  5
13. Which of the following is equal to  x  3 ?
2
a.
b.
c.
d.
e.
x2  9
x2  6 x  9
x2  9
x2  6 x  9
x2  6 x  9
14. If one of the factors of x 2  4 x  12 is ( x  6) what is the other factor?
a.
b.
c.
( x  4)
( x  2)
( x  2)
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d.
e.
( x  6)
( x  6)
2
2
DO YOUR FIGURING HERE
15. Which of the following is the correct factorization of x 2  5 x  6 ?
a.
b.
c.
d.
 x  6 x 1
 x 1 x  6
 x  3 x  2
 x  3 x  2
e. cannot be factored
16. Which of the following is a factorization of 25 x2  16 ?
a.
b.
c.
d.
e.
 5x  4 5x  4
2
 5x  4
 5x  16  5x  1
2
 5x  4
 5x  16  5 x  1
17. Which of the following is a correct factorization of 10 x 2  19 x  6 ?
a.
b.
c.
d.
e.
 2 x  2 5x  3
 5x  2 2 x  3
 5x  3 2 x  2
10 x  6 x  1
10 x  1 x  6
18. Which of the following is equal to  2 x  3 ?
2
a.
b.
c.
d.
e.
4x2  9
4 x 2  12 x  9
4 x2  9
4 x 2  12 x  9
4 x 2  10 x  9
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Education. May 2007
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19. What is the factorization of 4a 3  2a 2  8 ?
a.
2  2a 3  2a 2  4 
b.
2  2a 3  a 2  4 
c.
2a2  2a 1  4
d.
a2  4a  1  4
e. none of these
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