Name: 
 

Algebra 1 Chapter 9


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
2 – 11x2 – 8x + 6x2
a.
–5x2 – 8x + 2; quadratic trinomial
c.
–6x2 – 8x – 2; cubic polynomial
b.
5x2 – 8x – 2; quadratic trinomial
d.
6x2 – 8x + 2; cubic trinomial
 

 2. 
Write the polynomial in standard form.
4g – g3 + 3g2 – 2
a.
–2 + 4g + 3g2 – g3
c.
3g3 – g2 + 4g – 2
b.
g3 – 3g2 + 4g – 2
d.
–g3 + 3g2 + 4g – 2
 
 
Find the degree of the monomial.
 

 3. 
7m6n5
a.
5
b.
11
c.
6
d.
7
 

 4. 
6x8y5
a.
5
b.
6
c.
13
d.
8
 

 5. 
Match the expression with its name.
6x3 – 9x + 3
a.
cubic trinomial
c.
fourth-degree monomial
b.
quadratic binomial
d.
not a polynomial
 

 6. 
Write the perimeter of the figure.
mc006-1.jpg
a.
9x + 7x
b.
11x + 3x + 2
c.
14x + 2
d.
14x
 
 
Simplify the difference.
 

 7. 
(–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
a.
2x4 + 2x + 8
c.
–14x4 – 10x + 10
b.
–14x4 + 10x + 10
d.
2x4 + 2x + 10
 

 8. 
(4w2 – 4w – 8) – (2w2 + 3w – 6)
a.
2w2 – 7w – 2
c.
2w2 – 1w – 14
b.
6w2 – 1w – 14
d.
6w2 + 7w + 2
 

 9. 
Simplify the sum.
(4u3 + 4u2 + 2) + (6u3 – 2u + 8)
a.
10 – 2u + 4u2 + 10 u3
c.
–2u3 + 4u2 – 2u + 10
b.
–2u3 – 2u2 + 4u – 10
d.
10u3 + 4u2 – 2u + 10
 
 
Simplify the product.
 

 10. 
2n(n2 + 3n + 4)
a.
2n3 + 6n2 + 8n
c.
2n3 + 6n + 8
b.
2n3 + 3n + 4
d.
n2 + 5n + 4
 

 11. 
3p4(4p4 + 7p3 + 4p + 1)
a.
12p8 + 3p7 + 4p5 + p4
c.
7p8 + 10p7 + 7p5 + 4p4
b.
12p8 + 21p7 + 12p5 + 3p4
d.
12p16 + 21p12 + 15p4
 

 12. 
8x2(4x2 + 4y6)
a.
12x4 + 12x2y6
c.
12x4 + 12x2y6
b.
32x4 + 32x2y6
d.
32x4 + 32xy8
 

 13. 
7a3(5a6 – 2b3)
a.
12a9 – 9a3b6
c.
35a9 – 14a3b3
b.
35a9 – 14ab6
d.
12a18 – 9a3b6
 

 14. 
5a2(3a4 + 3b)
a.
8a4 + 8ab
c.
15a6 + 15a2b
b.
15a8 + 3b
d.
8a6 + 15a2b
 

 15. 
8p(–3p2 + 6p – 2)
a.
–5p3 + 14p2 – 6p
c.
14p2 – 6p – 5p3
b.
48p2 – 16p – 24p3
d.
–24p3 + 48p2 – 16p
 
 
Factor the polynomial.
 

 16. 
mc016-1.jpg
a.
2x(x2 + 2x + 4)
c.
x(2x2 + 4x + 8)
b.
2x(x + 2)(x + 4)
d.
2x3 + 4x2 + 8x
 

 17. 
24w12 + 64w8
a.
8w8(3w4 + 8)
c.
8(3w12 + 8w8)
b.
w8(24w4 + 64)
d.
8w7(3w5 + 8w)
 

 18. 
54c3d4 + 9c4d2
a.
9c3d2(d2 + 6c)
c.
9c4d2(d2 + 6)
b.
9c3d2(6d2 + c)
d.
9c4d2(6d2 + 1)
 

 19. 
Find the GCF of the terms of the polynomial.
8x6 + 32x3
a.
x3
b.
8x3
c.
8x3
d.
8x6
 

 20. 
The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?
a.
6x2 – 55x + 104 ft2
c.
11x2 – 56x + 66 ft2
b.
x2 + 6x – 16 ft2
d.
12x2 – 50x + 50 ft2
 
 
Simplify the product using FOIL.
 

 21. 
(3x – 7)(3x – 5)
a.
9x2 + 6x + 35
c.
9x2 – 36x – 35
b.
9x2 + 36x + 35
d.
9x2 – 36x + 35
 

 22. 
mc022-1.jpg
a.
mc022-2.jpg
c.
mc022-4.jpg
b.
mc022-3.jpg
d.
mc022-5.jpg
 

 23. 
Simplify the product using the distributive property.
mc023-1.jpg
a.
mc023-2.jpg
c.
mc023-4.jpg
b.
mc023-3.jpg
d.
mc023-5.jpg
 

 24. 
Find the missing coefficient.
mc024-1.jpgmc024-2.jpgmc024-3.jpg
a.
65
b.
5
c.
–5
d.
–65
 

 25. 
Simplify using the horizontal method.
(2n2 + 4n + 4)(4n – 5)
a.
8n3 + 26n2 – 36n – 20
c.
8n3 + 4n2 – 6n – 20
b.
8n3 + 6n2 – 4n – 20
d.
8n3 – 6n2 + 36n – 20
 

 26. 
Simplify using the vertical method.
(2k + 3)(2k2 – 4k – 3)
a.
4k3 + 18k2 – 2k – 9
c.
4k3 + 14k2 – 6k – 9
b.
4k3 – 2k2 + 6k – 9
d.
4k3 – 2k2 – 18k – 9
 
 
Find the square.
 

 27. 
(2x – 6)2
a.
4x2 – 24x + 36
c.
4x2 + 36
b.
4x2 – 8x + 36
d.
4x2 – 12x + 36
 

 28. 
(4x – 6y3)2
a.
16x2 – 24xy3 + 36y6
c.
16x2 + 36y6
b.
16x2 – 48xy3 + 36y6
d.
16x2 – 4xy3 + 36y6
 

 29. 
mc029-1.jpg
a.
mc029-2.jpg
c.
mc029-4.jpg
b.
mc029-3.jpg
d.
mc029-5.jpg
 

 30. 
Find the area of the UNSHADED region. Write your answer in standard form.
mc030-1.jpg
a.
–2x2 + 10x + 25
c.
10x + 25
b.
x2 + 8x + 25
d.
x2 + 10x + 25
 

 31. 
Find 332 using mental math.
a.
1,089
b.
900
c.
999
d.
729
 
 
Find the product.
 

 32. 
(j + 7)(j – 7)
a.
j2 + 14j – 49
c.
j2 + 14j – 49
b.
j2 – 14j – 49
d.
j2 – 49
 

 33. 
(2n + 2)(2n – 2)
a.
4n2 – 4
c.
4n2 + 2n – 4
b.
4n2 – 4n – 4
d.
4n2 + 4n – 4
 

 34. 
(4p – 6)(4p + 6)
a.
16p2 – 36
c.
16p2 + 48p + 36
b.
16p2 – 48p – 36
d.
16p2 + 36
 

 35. 
(4m2 – 5)(4m2 + 5)
a.
16m3 – 25
c.
16m4 + 25
b.
16m2 – 25
d.
16m4 – 25
 
 
Complete.
 

 36. 
y2 + 15y + 56 = (y + 7)(y +mc036-1.jpg)
a.
–8
b.
8
c.
–7
d.
7
 

 37. 
z2 + 9z – 90 = (z – 6)(z +mc037-1.jpg)
a.
–9
c.
90
b.
15
d.
–15
 
 
Factor the expression.
 

 38. 
w2 + 18w + 77
a.
(w – 7)(w + 11)
c.
(w + 7)(w + 11)
b.
(w – 7)(w – 11)
d.
(w + 1)(w + 77)
 

 39. 
d2 + 10d + 9
a.
(d + 9)(d – 1)
c.
(d – 9)(d – 1)
b.
(d – 9)(d + 1)
d.
(d + 9)(d + 1)
 

 40. 
k2 + kf – 2f2
a.
(k – 2f)(k + f)
c.
(k + 2f)(k + f)
b.
(k + 2f)(k – f)
d.
(k – 2f)(k – f)
 

 41. 
x2 – 10xy + 24y2
a.
(x + 6y)(x + 4y)
c.
(x + 2y)(x – 12y)
b.
(x – 2y)(x + 12y)
d.
(x – 6y)(x – 4y)
 

 42. 
x2 – x – 42
a.
(x – 7)(x + 6)
c.
(x + 7)(x – 6)
b.
(x + 7)(x + 6)
d.
(x – 7)(x – 6)
 

 43. 
15x2 – 16xy+ 4y2
a.
(3x – 2y)(5x + 2y)
c.
(3x + 2y)(5x – 2y)
b.
(3x – 2y)(5x – 2y)
d.
(3x + 2y)(5x + 2y)
 

 44. 
12d2 + 4d – 1
a.
(6d + 1)(2d + 1)
c.
(6d – 1)(2d + 1)
b.
(6d – 1)(2d – 1)
d.
(6d + 1)(2d – 1)
 

 45. 
6x2 + 5x + 1
a.
(3x – 1)(2x – 1)
c.
(3x – 1)(2x + 1)
b.
(3x + 1)(2x – 1)
d.
(3x + 1)(2x + 1)
 

 46. 
mc046-1.jpg
a.
2(5x – 2)(2x + 3)
c.
(10x – 2)(4x + 3)
b.
2(5x + 2)(2x – 3)
d.
2(5x + 4)(2x – 3)
 

 47. 
21x2 + 55x + 14
a.
(3x + 7)(7x – 2)
c.
(3x – 7)(7x + 2)
b.
(3x + 7)(7x + 2)
d.
(3x – 7)(7x – 2)
 

 48. 
6g2 + 11g – 35
a.
(3g + 5)(2g + 7)
c.
(3g + 5)(2g – 7)
b.
(3g – 5)(2g + 7)
d.
(3g – 5)(2g – 7)
 

 49. 
36y2 – 84y – 147
a.
(2y + 7)(6y – 7)
c.
(2y – 7)(18y + 21)
b.
3(2y – 7)(6y + 7)
d.
3(2y + 7)(6y + 7)
 

 50. 
48g2 – 22gh – 15h2
a.
(6g + 5h)(8g – 3h)
c.
(6g – 5h)(8g + 3h)
b.
(6g + 5)(8g + 3h2)
d.
(6g – 5)(8g + 3)
 

 51. 
16j2 + 24j + 9
a.
(4j – 9)(4j + 1)
c.
(4j + 3)(4j – 3)
b.
(4j + 3)2
d.
(4j – 3)2
 

 52. 
16m2 – 24mn + 9n2
a.
(4m – 3n)(4m + 3n)
c.
(4m – 3n)2
b.
(16m – 3n)(m + 3n)
d.
(4m + 3n)2
 

 53. 
mc053-1.jpg
a.
mc053-2.jpg
c.
mc053-4.jpg
b.
mc053-3.jpg
d.
mc053-5.jpg
 

 54. 
mc054-1.jpg
a.
mc054-2.jpg
b.
mc054-3.jpg
c.
mc054-4.jpg
d.
mc054-5.jpg
 

 55. 
r2 – 49
a.
(r – 7)(r + 7)
c.
(r – 7)(r – 7)
b.
(r + 7)(r + 7)
d.
(r – 7)(r + 9)
 

 56. 
4x2 – 81y2
a.
(2x + 9)(2x – 9)
c.
(2x + 9y)2
b.
(2x + 9y)(2x – 9y)
d.
(2x – 9y)2
 

 57. 
k2 – 16h2
a.
(k + 4h)(k + 4h)
c.
h2(k + 4)(k – 4)
b.
(k – 4h2)(k + 4)
d.
(k + 4h)(k – 4h)
 

 58. 
49b2 – 36
a.
(6b + 7)(6b – 7)
c.
(7b + 6)(7b – 6)
b.
(7b + 6)(7b + 6)
d.
(7b – 6)(7b – 6)
 

 59. 
3x3 + 3x2 + x + 1
a.
x(3x2 + x + 1)
c.
3x2(x + 1)
b.
(x + 3)(3x2 – 1)
d.
(x + 1)(3x2 + 1)
 

 60. 
6g3 + 8g2 – 15g – 20
a.
(2g2 – 4)(3g + 5)
c.
(2g2 – 5)(3g + 4)
b.
(2g2 + 4)(3g – 5)
d.
(2g2 + 5)(3g – 4)
 

 61. 
50k3 – 40k2 + 75k – 60
a.
5(2k2 – 3)(5k + 4)
c.
(2k2 + 15)(5k – 20)
b.
(10k2 – 3)(25k + 4)
d.
5(2k2 + 3)(5k – 4)
 

 62. 
Find the radius of a circle with an area of mc062-1.jpg.
a.
3x – 4
b.
9x – 16
c.
16x + 9
d.
4x + 3
 

 63. 
Find the GCF of the first two terms and the GCF of the last two terms of the polynomial.
5h3 + 20h2 + 4h + 16
a.
5h2, 16
b.
5h3, 4
c.
5h2, 4
d.
h2, h
 

 64. 
Factor completely.
6x4 – 9x3 – 36x2 + 54x
a.
3x(x2 – 6)(2x – 3)
c.
6x(x2 – 6)(2x – 3)
b.
3x(x2 + 6)(2x + 3)
d.
6x(x2 + 6)(2x + 3)
 
 
Factor by grouping.
 

 65. 
3x2 + 7x – 6
a.
(3x – 2)(x – 3)
c.
(x + 3)(3x + 2)
b.
(3x – 2)(x + 3)
d.
(3x + 2)(x – 3)
 

 66. 
21m2 – 29m – 10
a.
(7m – 2)(3m – 5)
c.
(7m + 2)(3m – 5)
b.
(7m + 2)(3m + 5)
d.
(7m – 2)(3m + 5)
 

 67. 
a2 + ab – 56b2
a.
(a + 8b)(a + 7b)
c.
(a + 8b)(a – 7b)
b.
(a – 8)(a + 7b)
d.
(a – 8b)(a – 7b)
 

 68. 
40p2 – 13p – 36
a.
(8p + 9)(5p + 4)
c.
(8p – 9)(5p + 4)
b.
(8p – 9)(5p – 4)
d.
(8p + 9)(5p – 4)
 

Short Answer
 

 69. 
a. Find the surface area of the cube.
b. Find the volume of the cube.

sa069-1.jpg
 

 70. 
Suppose you are playing a game with two number cubes. Let A represent rolling 2, 3, or 4, and B represent rolling 1, 5, or 6. The probability of A is sa070-1.jpg and the probability of B is sa070-2.jpg.
a.Simplify sa070-3.jpg
b.What is the probability that one number cube shows 2, 3, or 4, and the other shows 1, 5, or 6?
 

 71. 
Factor the following trinomial.
w18 – 9w9y5 + 14y10
 

 72. 
Factor the following expression.
198q3r2 – 184q2r2 + 18qr2
 

 73. 
Find a pair of factors for each number by using the difference of two squares.
a.45
b.77
c.112
 

Essay
 

 74. 
Find the area of the shaded region. Show all your work.
es074-1.jpg
 

 75. 
Explain how to factor the following trinomial.
g4 + 4g2j – 60j2
 

 76. 
Factor the expression by grouping. Show your work.
24q7 – 42q4r + 36q3r2 – 63r3
 

Other
 

 77. 
Explain how to factor the following expression.
66r2h + 57rh + 12h
 

 78. 
Let a2 – 2a – 24 = (a + b)(a + c). Explain what you can determine about the signs of b and c, and also explain what you can determine about the absolute values of a and b.
 

 79. 
Explain the advantages of the vertical and horizontal methods of multiplying a binomial and a trinomial.
 

 80. 
Can you write a binomial in standard form with a degree of 0? Can you write a binomial with a degree of 3? Explain.
 



 
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