Name: ________________________ Class: ___________________ Date: __________ ID: A

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Chapter 5 Practice Test

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Factor the binomial 15y 2 − 48y.

a. 3(5y 2 − 16y) c. y(15y − 48)b. 3y(5y − 16y) d. 3y(5y − 16)

____ 2. Factor the trinomial 4 − 8n + 12n 2 .a. 4(−2n + 3n 2) c. 2(2 − 4n + 6n 2)b. 4(1 − 2n + 3n 2) d. 4(1 + 2n + 3n 2)

____ 3. Factor the trinomial −24c 3d − 40c2 d 2 − 32cd 3 .a. −8cd(3c2 − 5cd − 4d 2) c. 8cd(−3c2 + 5cd + 4d 2)b. 8cd(3c 2 + 5cd + 4d 2) d. −8cd(3c2 + 5cd + 4d 2)

____ 4. Factor the binomial −10m2 − 40m4 .a. −10m2(1 + 4m2 ) c. −10(m2 + 4m4)b. −10m2(4m2) d. −5m2 (2 + 8m2)

____ 5. Identify the greatest common factor of the terms in the trinomial 6s3 t4 + 12s4 t2 − 15s2 t3 .a. 6s2 t2 c. 3s2 t3

b. 3s2 t2 d. 3s3 t2

____ 6. Factor the trinomial 20a 2 b − 25ab + 45ab 2 .a. 5ab(4a − 5 + 9b) c. ab(20a − 25 + 45b)b. 5ab(4a − 5ab + 9b) d. 5(4a 2 b − 5ab + 9ab 2)

____ 7. Which expression represents the area of the shaded region?

a. 2r(2r − π) b. r2(1 − π) c. r2(4 − π) d. r(r − 2π)

Name: ________________________ ID: A

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____ 8. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.a. y 2 + 3y + 12 c. y 2 + 8y + 15b. y 2 + 12y + 5 d. y 2 + 14y + 3

____ 9. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.a. 2a 2 + 29a + 12 c. 2a 2 + 14a + 63b. 2a 2 + 19a + 9 d. 2a 2 + 9a + 2

____ 10. Expand and simplify: (4 − r)(7 − r) a. 28 − 11r + r2 c. 28 + 3r + r2

b. 28 − 3r + r2 d. 28 + 11r + r2

____ 11. Factor: v 2 − 13v + 36a. (v + 3)(v + 12) c. (v − 4)(v − 9)b. (v − 3)(v − 12) d. (v + 4)(v + 9)

____ 12. Factor: −24 − 2x + x 2

a. (6 + x)(−4 + x) c. (−3 + x)(8 + x)b. (3 + x)(−8 + x) d. (−6 + x)(4 + x)

____ 13. Factor: −3b 2 + 15b + 18a. −3(b − 2)(b + 3) c. −3(b − 1)(b + 6)b. −3(b + 2)(b − 3) d. −3(b + 1)(b − 6)

____ 14. Factor: −4d 2 − 28d + 240a. −4(d + 3)(d − 20) c. −4(d − 3)(d + 20)b. −4(d + 5)(d − 12) d. −4(d − 5)(d + 12)

____ 15. Complete: (a + 6)(a − ) = a 2 + a − 12

a. (a + 6)(a − 4) = a 2 + 4a − 12 c. (a + 6)(a − 2) = a 2 + 2a − 12b. (a + 6)(a − 2) = a 2 + 4a − 12 d. (a + 6)(a − 4) = a 2 + 2a − 12

____ 16. Factor: c 2 − 4c − 117a. (c − 9)(c + 13) c. (c + 9)(c − 13)b. (c − 3)(c + 39) d. (c + 3)(c − 39)

____ 17. Factor: 12 − 4g − g 2

a. (4 − g)(3 + g) c. (6 − g)(2 + g)b. (6 + g)(2 − g) d. (4 + g)(3 − g)

____ 18. Expand and simplify: (h − 6)(h + 11) a. h 2 − 5h − 66 c. h 2 + 17h − 66b. h 2 + 5h − 66 d. h 2 − 17h − 66

Name: ________________________ ID: A

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____ 19. Complete. (k − )(k − 5) = k 2 − k + 135

a. (k − 27)(k − 22) = k 2 − 5k + 135 c. (k − 27)(k − 32) = k 2 − 5k + 135b. (k − 27)(k − 5) = k 2 − 32k + 135 d. (k − 27)(k − 5) = k 2 − 22k + 135

____ 20. Factor: −5m2 + 20m + 60a. −5(m + 2)(m − 6) c. −5(m − 4)(m + 3)b. −5(m − 2)(m + 6) d. −5(m + 4)(m − 3)

____ 21. Which multiplication sentence does this set of algebra tiles represent?

a. (2x − 2)(2x + 2) c. (2x 2 + 2x)(2x2 + 2x)b. (2x 2 + 2)(2x 2 + 2) d. (2x + 2)(2x + 2)

____ 22. Which set of algebra tiles represents 3x 2 + x + 4?

a. c.

b. d.

____ 23. Factor: 24b 2 + 50b − 14a. 2(4b − 1)(3b + 7) c. 2(4b − 7)(3b + 1)b. 2(4b + 7)(3b + 1) d. 2(4b + 1)(3b − 7)

____ 24. Expand and simplify: 3(1 − 2t)(9 + 4t) a. −24t2 + 42t + 27 c. −72t2 − 126t + 81b. −24t2 + 66t + 27 d. −24t2 − 42t + 27

Name: ________________________ ID: A

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____ 25. Factor: 4 − 9z − 13z2

a. (2 − 13z)(2 + z) c. (2 + 13z)(2 − z)b. (4 − 13z)(1 + z) d. (4 + 13z)(1 − z)

____ 26. Which polynomial, written in simplified form, represents the area of this rectangle?

a. 8x2 − 36xy − 20y2 c. 16x 2 + 72xy − 40y 2

b. 8x2 + 22xy − 20y2 d. 8x2 + 36xy − 20y2

____ 27. Expand and simplify: (6x − y)(3x + 8y) − (2x − 3y)2

a. 14x 2 + 51xy − 17y 2 c. 14x 2 + 57xy + 1y2

b. 14x 2 + 33xy + 1y2 d. 14x 2 + 57xy − 17y 2

____ 28. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region.

a. 5x2 + 31x + 66 c. 5x2 + 31x + 30b. 5x2 + 37x + 30 d. 5x2 + 37x + 66

____ 29. Factor: 16p 2 − 81q 2

a. (4p − 9q)2 c. (16p − 9q)(p − 9q)b. (4p + 9q)2 d. (4p + 9q)(4p − 9q)

____ 30. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.9a 2 + 9a + 36a. Difference of squares c. Neitherb. Perfect square trinomial

____ 31. Identify this polynomial as a perfect square trinomial, a difference of squares, or neither.25g 2 − 9h 2

a. Perfect square trinomial c. Neitherb. Difference of squares

Name: ________________________ ID: A

5

____ 32. Factor: 3z4 − 768z2

a. 3z2 (z + 16)(z − 16) c. z2(z + 48)(z − 16)b. 3z2 (z + 16)2 d. 3z2 (z − 16)2

____ 33. Factor: 162 − 2w4

a. (9 − w2)(18 − w2 ) c. 2(9 − w2)2

b. 2(9 + w2)(3 + w)(3 − w) d. 2(9 + w2)2

____ 34. Determine the area of the shaded region in factored form.

a. 4(x + 12) c. (3x + 12)(x + 2)b. (3x + 2)(x + 12) d. (3x − 2)(x − 12)

Short Answer

35. Factor the binomial 85x 3 − 20x.

36. Factor the trinomial 8m2 n − 18n 2 − 2mn.

37. Write an expression for the width of this rectangle.

38. Identify the greatest common factor of the terms in this set. 8x2 y, 24y 2 , 18xy

39. Factor: s2 − 33s + 32

Name: ________________________ ID: A

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40. Find and correct the errors in this factorization.w2 − 2w − 80 = w − 8� � w + 10� �

41. Find and correct the error(s) in this solution of factoring by decomposition.90y 2 + 77y − 52 = 90y 2 + 117y − 40y − 52 = 9y(10y + 13) + 4(10y + 13) = (10y + 13)(9y + 4)

42. Copy and complete this statement.

(60a − 25)(a − 385) = − + 9625

43. Find and correct the errors in this solution.(11a + b)(2a − 13b + 4)= 13a 2 − 143ab + 44a − 2ab − 13b 2 + 4b= 13a 2 − 145ab − 13b 2 − 44a + 4b

44. Expand and simplify. (5r − 6s + s2)(13r + 3s − 5s2)

45. Factor: 49s2 − 64t2

46. Find an integer to replace � so that the trinomial is a perfect square.121x 2 − 308xy + y 2

47. The area of a square is represented by the trinomial 36m2 + 84mn + 49n 2 . Determine an expression for the perimeter of the square.

Problem

48. A square is drawn inside a circle with radius 11x. a) Write an expression for the area of the shaded region.b) Factor the expression.

Name: ________________________ ID: A

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49. Find the area of the rectangle.

50. Use decomposition to factor 81y 2 + 36y + 4. Explain your steps.

51. A rectangle has length 14x and width y. Strips of width x − 8 are cut from the rectangle as shown. Write an expression that represents the area of the rectangle that remains.

52. Factor. Explain your steps.196x 2 − 16y 2

53. A picture and its frame have dimensions as shown. a) Find an expression for the area of the frame, in factored form. b) Determine the area of the frame when s = 15 cm.

ID: A

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Chapter 5 Practice TestAnswer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

2. ANS: B PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

3. ANS: D PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

4. ANS: A PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

5. ANS: B PTS: 1 DIF: Easy REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

6. ANS: A PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

7. ANS: C PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a Polynomial LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

8. ANS: C PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

9. ANS: B PTS: 1 DIF: Easy REF: 3.4 Modelling Trinomials as Binomial Products LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

10. ANS: A PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

11. ANS: C PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

12. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

13. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

14. ANS: D PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

ID: A

2

15. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

16. ANS: C PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

17. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

18. ANS: B PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

19. ANS: B PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

20. ANS: A PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

21. ANS: D PTS: 1 DIF: Easy REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

22. ANS: B PTS: 1 DIF: Easy REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

23. ANS: A PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

24. ANS: D PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN4TOP: Algebra and Number KEY: Procedural Knowledge

25. ANS: B PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + c LOC: 10.AN5TOP: Algebra and Number KEY: Procedural Knowledge

26. ANS: D PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

27. ANS: D PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

28. ANS: A PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

29. ANS: D PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

30. ANS: C PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

31. ANS: B PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

32. ANS: A PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

ID: A

3

33. ANS: B PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

34. ANS: B PTS: 1 DIF: Difficult REF: 3.8 Factoring Special PolynomialsLOC: 10.AN4 | 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

SHORT ANSWER

35. ANS: 5x(17x2 − 4)

PTS: 1 DIF: Easy REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

36. ANS: 2n(4m2 − 9n − m)

PTS: 1 DIF: Easy REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

37. ANS: a + 6b

PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

38. ANS: 2y

PTS: 1 DIF: Moderate REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

39. ANS: s − 32� � s − 1� �

PTS: 1 DIF: Easy REF: 3.5 Polynomials of the Form x^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

40. ANS: w2 − 2w − 80 = w + 8� � w − 10� �

PTS: 1 DIF: Moderate REF: 3.5 Polynomials of the Form x^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

41. ANS: 90y 2 + 77y − 52 = 90y 2 + 117y − 40y − 52 = 9y(10y + 13) − 4(10y + 13) = (10y + 13)(9y − 4)

PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

ID: A

4

42. ANS: (60a − 25)(a − 385) = 60a 2 − 23 125a + 9625

PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

43. ANS: (11a + b)(2a − 13b + 4)= 22a 2 − 143ab + 44a + 2ab − 13b 2 + 4b= 22a 2 − 141ab + 44a − 13b 2 + 4b

PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

44. ANS: 65r2 − 63rs − 12rs2 − 18s2 + 33s3 − 5s4

PTS: 1 DIF: Moderate REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Procedural Knowledge

45. ANS: 7s + 8t� � 7s − 8t� �

PTS: 1 DIF: Easy REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

46. ANS: 196

PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

47. ANS: 4 6m + 7n� �

PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Procedural Knowledge

ID: A

5

PROBLEM

48. 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.A = πr2

A = π(11x)2

A = 121πx 2

To determine the area of the square, first determine the side length, s, of the square.Use the Pythagorean Theorem in right ∆ABC.s2 = AB2 + BC2

s2 = (11x)2 + (11x)2

s2 = 121x2 + 121x 2

s2 = 242x2

s = 242x 2

Use the formula for the area, A, of a square.A = s2

A = 242x 2�

�

�����

�

�

�����

2

A = 242x2

The area, A, of the shaded region is:.A = 121πx 2 − 242x 2

b) 121πx 2 − 242x 2 = 121x 2(π − 2)

PTS: 1 DIF: Difficult REF: 3.3 Common Factors of a PolynomialLOC: 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills

ID: A

6

49. ANS: Use the formula for the area, A, of a rectangle. A = l × w

A = 5b − 6� � 3b − 2� �

Use the distributive property. A = 5b(3b − 2) + (−6)(3b − 2)

A = 15b 2 − 10b − 18b + 12

A = 15b 2 − 28b + 12

The area of the rectangle is 15b 2 − 28b + 12 square units.

PTS: 1 DIF: Moderate REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills

ID: A

7

50. ANS: 81y 2 + 36y + 4

Check for common factors; there are none.

The product of the coefficient of y2 and the constant term is: 81(4) = 324

Write 36y as the sum of two terms whose coefficients have a product of 324.

Factors of 324 Sum of Factors

1, 324 1 + 324 = 325

2, 162 2 + 162 = 164

3, 108 3 + 108 = 111

4, 81 4 + 81 = 85

6, 54 6 + 54 = 60

9, 36 9 + 36 = 45

12, 27 12 + 27 = 39

18, 18 18 + 18 = 36

The two coefficients are 18 and 18, so write the trinomial 81y 2 + 36y + 4 as 81y 2 + 18y + 18y + 4.

Remove a common factor from the 1st pair of terms, and from the 2nd pair of terms.81y 2 + 18y + 18y + 4 = 9y(9y + 2) + 2(9y + 2)

Each product has a common binomial factor.81y 2 + 18y + 18y + 4 = (9y + 2)(9y + 2)

So, 81y 2 + 36y + 4 = (9y + 2)(9y + 2)

PTS: 1 DIF: Difficult REF: 3.6 Polynomials of the Form ax^2 + bx + cLOC: 10.AN5 TOP: Algebra and Number KEY: Communication | Problem-Solving Skills

ID: A

8

51. ANS: The length of the rectangle that remains is:14x − (x − 8) = 14x − x + 8 = 13x + 8

The width of the rectangle that remains is: y − (x − 8) = y − x + 8

Use the formula for the area, A, of a rectangle:A = lw

A = (13x + 8)(y − x + 8)

A = 13x(y) + 13x(−x) + 13x(8) + 8(y) + 8(−x) + 8(8)

A = 13xy − 13x 2 + 104x + 8y − 8x + 64

A = 13xy − 13x 2 + 96x + 8y + 64

The expression 13xy − 13x 2 + 96x + 8y + 64 represents the area of the rectangle that remains.

PTS: 1 DIF: Difficult REF: 3.7 Multiplying PolynomialsLOC: 10.AN4 TOP: Algebra and Number KEY: Problem-Solving Skills

52. ANS: 196x 2 − 16y 2

As written, each term of the binomial is not a perfect square. But the terms have a common factor 4. Remove this common factor.

196x 2 − 16y 2

= 4(49x 2 − 4y 2)

Write each term in the binomial as a perfect square.

4(49x 2 − 4y 2) = 4 (7x)2 − (2y)2

�����

�

����� Write these terms in binomial factors.

= 4(7x − 2y)(7x + 2y)

PTS: 1 DIF: Moderate REF: 3.8 Factoring Special PolynomialsLOC: 10.AN5 TOP: Algebra and Number KEY: Communication | Problem-Solving Skills

ID: A

9

53. ANS: a) The area, A, of the larger square is: 8s� �

2 = 64s2

The area, A, of the smaller square is: (8s − 4 − 4)2 = 8s − 8� �2

= 64s2 − 128s + 64

The area, A, of the frame is: A = 64s2 − (64s2 − 128s + 64)

A = 64s2 − 64s2 + 128s − 64

A = 128s − 64

A = 64(2s − 1)

b) When s = 15 cm, the area, A square centimetres, of the frame is:A = 64(2s − 1)

A = 64 2 15� � − 1���

� ���

A = 1856The area of the frame is 1856 cm2 .

PTS: 1 DIF: Difficult REF: 3.8 Factoring Special PolynomialsLOC: 10.AN4 | 10.AN5 TOP: Algebra and Number KEY: Problem-Solving Skills