Math 1201
Unit 3 – Factors and Products
Final Review
Multiple Choice
____
____
____
____
____
1. Factor the binomial
a.
b.
.
2. Factor the binomial
a.
b.
.
3. Factor the trinomial
a.
b.
c.
d.
.
c.
d.
4. Factor the trinomial
a.
b.
.
c.
d.
5. Factor the trinomial
a.
b.
____
6. Factor the trinomial
a.
b.
____
7. Factor the binomial
a.
b.
____
c.
d.
.
c.
d.
.
c.
d.
.
c.
d.
8. Simplify the expression
a.
, then factor.
c.
b.
____
9. Factor the trinomial
a.
b.
d.
.
c.
d.
____ 10. Identify the greatest common factor of the terms in the trinomial
a.
c.
b.
d.
____ 11. Factor the trinomial
a.
b.
____ 12. Factor the trinomial
a.
b.
____ 13. Simplify the expression
a.
b.
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.
.
c.
d.
.
c.
d.
, then factor.
c.
d.
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Math 1201
Unit 3 – Factors and Products
Final Review
____ 14. Which expression represents the area of the shaded region?
a.
b.
c.
d.
____ 15. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.
a.
c.
b.
d.
____ 16. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.
a.
c.
b.
d.
____ 17. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.
a.
c.
b.
d.
____ 18. Expand and simplify:
a.
b.
c.
d.
____ 19. Expand and simplify:
a.
b.
c.
d.
____ 20. Factor:
a.
b.
c.
d.
____ 21. Factor:
a.
b.
c.
d.
____ 22. Factor:
a.
b.
c.
d.
____ 23. Factor:
a.
b.
c.
d.
____ 24. Factor:
a.
b.
c.
d.
____ 25. Factor:
a.
b.
c.
d.
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Math 1201
Unit 3 – Factors and Products
Final Review
____ 26. Which multiplication sentence does this set of algebra tiles represent?
a.
b.
____ 27. Which set of algebra tiles represents
a.
b.
c.
d.
?
c.
d.
____ 28. Expand and simplify:
a.
b.
c.
d.
____ 29. Expand and simplify:
a.
b.
c.
d.
____ 30. Factor:
a.
b.
c.
d.
____ 31. Expand and simplify:
a.
b.
c.
d.
____ 32. Factor:
a.
b.
c.
d.
____ 33. Expand and simplify:
a.
b.
c.
d.
____ 34. Expand and simplify:
a.
b.
c.
d.
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Math 1201
Unit 3 – Factors and Products
Final Review
____ 35. Which polynomial, written in simplified form, represents the area of this rectangle?
8x – 4y
x + 5y
a.
b.
c.
d.
____ 36. Expand and simplify:
a.
b.
c.
d.
____ 37. Expand and simplify:
a.
b.
c.
d.
____ 38. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region.
a.
b.
____ 39. Factor:
a.
b.
c.
d.
c.
d.
____ 40. Factor:
a.
b.
c.
d.
____ 41. Factor:
a.
b.
c.
d.
____ 42. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.
a. Perfect square trinomial
b. Difference of squares
____ 43. Factor:
a.
b.
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c. Neither
c.
d.
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Math 1201
Unit 3 – Factors and Products
Final Review
____ 44. Determine the area of the shaded region in factored form.
a.
b.
c.
d.
Short Answer
45. Factor the binomial
.
46. Factor the trinomial
.
47. Write an expression for the width of this rectangle.
2a
Area = 2a 2+ 12ab
48. Simplify
, then factor.
49. Identify the greatest common factor of the terms in this set.
50. Expand and simplify:
51. Factor:
52. Find and correct the errors in this factorization.
53. Expand and simplify:
54. Factor:
55. Factor:
56. Find and correct the error(s) in this solution of factoring by decomposition.
57. Expand and simplify:
58. Factor:
59. Factor:
60. Factor fully:
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Math 1201
Unit 3 – Factors and Products
61. The area of a square is represented by the trinomial
perimeter of the square.
Final Review
. Determine an expression for the
Problem
62. 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?
63. A square is drawn inside a circle with radius
.
a) Write an expression for the area of the shaded region.
b) Factor the expression.
64. This composite object is formed by a cone with a hemisphere on top. A formula for the volume of this object
is:
r
h
a) Factor this formula.
b) Use both forms of the formula to calculate the volume of this composite object with radius 4 cm and
height 10 cm.
c) Which formula to do you prefer to use? Why?
65. Factor. Check by expanding.
66. Factor. Check by expanding.
67. Find the area of the rectangle.
5b – 6
3b – 2
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Math 1201
Unit 3 – Factors and Products
Final Review
Answers - MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
ANS:
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ANS:
C
D
B
C
D
B
A
B
C
B
A
B
B
C
C
D
B
A
A
C
C
D
D
C
B
D
B
B
A
B
D
A
C
C
D
A
C
A
D
D
D
B
A
B
SHORT ANSWER
45.
ANS:
46.
ANS:
47.
ANS:
48.
ANS:
49.
ANS:
50.
ANS:
51.
ANS:
52.
ANS:
53.
ANS:
54.
ANS:
55.
ANS:
56.
ANS:
57.
ANS:
58.
ANS:
59.
ANS:
60.
ANS:
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Math 1201
61.
Unit 3 – Factors and Products
Final Review
ANS:
PROBLEM
62.
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)
63.
The student should have expanded her solutions to check that the trinomial was the same as the original trinomial each time.
ANS:
a) The area of the shaded region is the area of the circle minus the area of the square.
Use the formula for the area of a circle.
To determine the area of the square, first determine the side length, s, of the square.
Use the Pythagorean Theorem in
right ∆ABC.
Use the formula for the area, A, of a square.
The area, A, of the shaded region is:.
b)
64.
ANS:
a)
Factor each term of the binomial.
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Math 1201
Unit 3 – Factors and Products
Final Review
b)
c)
65.
Answers will vary.
For example: I prefer to use the factored formula because it has only one fraction.
ANS:
Two numbers with a sum of 1 and a product of
are 7 and
.
So,
Check that the factors are correct. Multiply the factors.
This trinomial is the same as the original trinomial, so the factors are correct.
66.
ANS:
The greatest common factor is 8.
Two numbers with a sum of
and a product of 45 are
.
Check that the factors are correct. Multiply the factors.
The trinomial is the same as the original trinomial, so the factors are correct.
67.
ANS:
Use the formula for the area, A, of a rectangle.
Use the distributive property.
The area of the rectangle is
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square units.
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