Download Math 1201 Factoring Review Name

Math 1201 Factoring Review
Name:______________________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Factor the binomial
a.
b.
____
2. Factor the trinomial
a.
b.
____
3. Factor the binomial
a.
b.
____
____
____
____
____
c.
d.
.
c.
d.
.
c.
d.
4. Factor:
a.
b.
c.
d.
5. Factor:
a.
b.
c.
d.
6. Factor:
a.
b.
c.
d.
7. Which set of algebra tiles represents
a.
?
c.
b.
____
.
d.
8. Expand and simplify:
a.
b.
c.
d.
9. Factor:
a.
b.
c.
d.
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____ 10. Expand and simplify:
a.
b.
c.
d.
____ 11. Expand and simplify:
a.
b.
c.
d.
____ 12. Expand and simplify:
a.
b.
c.
d.
____ 13. Which polynomial, written in simplified form, represents the area of this rectangle?
8x – 4y
x + 5y
a.
b.
c.
d.
____ 14. Expand and simplify:
a.
b.
c.
d.
____ 15. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region.
3x + 8
x +6
x –3
a.
b.
____ 16. Factor:
a.
b.
2x + 6
c.
d.
c.
d.
____ 17. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.
a. Perfect square trinomial
b. Difference of squares
c. Neither
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____ 18. Factor:
a.
b.
c.
d.
____ 19. Factor:
a.
b.
c.
d.
____ 20. Determine the area of the shaded region in simplified form then factored form. (Both figures are squares)
x–5
2x + 7
a.
b.
c.
d.
Short Answer
21. Write an expression for the width of this rectangle.
2a
Area = 2a 2+ 12ab
22. Expand and simplify:
23. Expand and simplify:
24. Factor:
25. a) Here are a student’s solutions for factoring polynomials. Identify the errors in each solution. Write a correct
solution.
i) Factor:
Solution:
ii) Factor:
Solution:
b) What should the student have done to check her work?
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26. Multiply this pair of binomials. Sketch and label a rectangle to illustrate the product.
27. Factor
.
28. factor
.
29. Write a polynomial to represent the area of this rectangle. Simplify the polynomial.
6x + 3y
4x – 5y
30. The volume of a right rectangular prism is represented by the trinomial
Use factoring to determine the length and width of the prism when the height is
.
. (V=lwh)
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Math 1201 Factoring Review Answer Section
MULTIPLE CHOICE
1. ANS: C
2.ANS:B
3.ANS:A
4.ANS:C
5. ANS: D
6.ANS:D
7.ANS:B
8.ANS:B
10. ANS: D
11.ANS:C
12.ANS:A
13.ANS:D
14. ANS: D
15.ANS:A
16.ANS:D
17.ANS:B
18. ANS: A
19.ANS:B
20.ANS:B
SHORT ANSWER
21. ANS:
22.ANS:
23.ANS:
24. ANS:
25. ANS: a) i) Correction:
The student did not remove the common factor from the third term correctly. When the common factor is
the same as the term, a factor of 1 remains. This must be written as a term in the factored polynomial.
ii) Correction:
When the student removed the common factor from the third term, she made a sign error. The sign
should be negative, not positive.
b) The student should have expanded her solutions to check that the trinomial was the same as the original
trinomial each time.
26.
x
x
(x)(x) =x 2
9
(9)(x) = 9x
–4 (–4)(x) = –4x (–4)(9) = –36
27.
28.
29.
30.
When the height of the prism is
, both the length and width are
.
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