Chapter 6 Factor completely, or state that the polynomial is prime

Solve the problem.

54)

Find a formula for the area of the shaded grey region and express it in factored form.

7x

1

A)

(x +7)(x –7)

B)

7x – 1

C)

(7x + 1)(7x – 1)

D)

(7x – 1)(7x – 1)

Factor completely. If unfactorable, indicate that the polynomial is prime.

55)

(x +6)2–16

55)

A)

(x + 22)(x – 10)

B)

x2+ 12x + 20

C)

(x + 10)(x + 2)

D)

(x – 2)(x – 10)

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is

prime.

56)

x6– 3x5– 18x4

56)

A)

x4(x – 3)(x – 6)

B)

x4(x + 3)(x – 6)

C)

x4(x + 3)(x + 6)

D)

x3(x2– 3x – 18)

Solve the problem.

57)

The model of a building has the shape of a rectangular solid. The height is represented by x

inches. The base of the model is square and the volume of the model is x3–60x2+900x. Express

the area of the model‘s base in terms of x.

x inches

A)

(x +30)(x –30) square inches

B)

x2–900 square inches

C)

(x –30)2 square inches

D)

60x square inches

58)

The equation D =1

2n(n – 3) gives the number of diagonals D for a polygon with n sides. Use this

equation to solve the problem. Find the number of sides n for a polygon that has 90 diagonals.

58)

A)

16 sides

B)

3 sides

C)

15 sides

D)

12 sides

Factor by grouping.

59)

x2– 4x – 3x + 12

59)

A)

(x – 3)(x + 8)

B)

(x + 3)(x – 4)

C)

(x – 3)(x – 4)

D)

–7x(x2+ 12)

16

Solve the problem.

60)

An object is thrown upward from the top of a 160–foot building with an initial velocity of 48 feet

per second. The height h of the object after t seconds is given by the quadratic equation

h = – 16t2+

48t + 160. When will the object hit the ground?

A)

2 sec

B)

160 sec

C)

–2 sec

D)

5 sec

Factor completely. If unfactorable, indicate that the polynomial is prime.

61)

z2–49

61)

A)

(z –7)2

B)

(z +7)2

C)

prime

D)

(z +7)(z –7)

Factor completely, or state that the polynomial is prime.

62)

x2– 7x + 12

62)

A)

(x + 4)(x – 3)

B)

(x – 4)(x – 3)

C)

prime

D)

(x + 4)(x + 1)

Factor completely. If unfactorable, indicate that the polynomial is prime.

63)

3x7+

12x6+ 12x5

63)

A)

x7(3x + 6)(x + 2)

B)

3x7(x2+ 4x + 4)

C)

3x7(x – 2)2

D)

3x5(x + 2)2

17

Factor out the GCF from the polynomial.

64)

8x + 8

A)

64x

B)

8(x + 1)

C)

8x + 1

D)

8(x + 8)

Factor completely. If unfactorable, indicate that the polynomial is prime.

65)

x2+ 23x + 24

65)

A)

prime

B)

(x + 24)(x – 1)

C)

(x – 8)(x + 3)

D)

(x + 8)(x – 3)

Factor.

66)

48m6– 48m4– 42m2

66)

A)

–m2(–48m4– 48m2+ 42)

B)

m2(48m4– 48m2– 42)

C)

6m2(8m4– 8m2– 7)

D)

6(8m6– 8m4– 7m2)

Factor completely. If unfactorable, indicate that the polynomial is prime.

67)

49x2– 16

67)

A)

(7x + 4)2

B)

prime

C)

(7x – 4)2

D)

(7x + 4)(7x – 4)

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is

prime.

68)

6x2– 21x – 12

68)

A)

3(2x + 1)(x – 4)

B)

3(2x – 1)(x + 4)

C)

prime

D)

(6x – 3)(x + 4)

Solve the problem.

69)

Express the total shaded area as the product of two binomials.

x 3

3

16x

8x

(The figures are not drawn to scale.)

A)

(4x +3)(4x –3)

B)

(4x +3)(16x2–24x +9)

C)

(4x +3)2

D)

(3x +4)2

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is

prime.

70)

25x3y4+30x2y5+8xy6

70)

A)

x(5xy4+4y5)(5x +2y)

B)

y4(5x +4y)(5x2+2xy)

C)

prime

D)

xy4(5x +4y)(5x +2y)

19

Factor out the GCF from the polynomial.

71)

15m8+ 9m4– 6m2

71)

A)

m2(15m6+ 9m2– 6)

B)

3(5m8+ 3m4– 2m2)

C)

cannot be factored

D)

3m2(5m6+ 3m2– 2)

Factor completely. If unfactorable, indicate that the polynomial is prime.

72)

100a2+ 0a – 36

72)

A)

(20a + 12)(5a – 3)

B)

(5a + 3)(20a – 12)

C)

4(5a + 3)(5a – 3)

D)

4(5a – 3)(5a + 3)

Factor out the GCF from the polynomial.

73)

17x4– 13x6

73)

A)

17x41 –13

17 x2

B)

17(x4– 221)

C)

x4(1 – 13x2)

D)

x4(17 – 13x2)

Solve the equation.

74)

x2+ 7x – 30 = 0

74)

A)

{–10, 3}

B)

{–3, 10}

C)

{3, 10}

D)

{–10, 1}

20

Factor completely.

75)

x4–x

64

75)

A)

x2–1

4x2+1

16 x +1

64

B)

x x +1

4x2–1

4x +1

16

C)

x x2–1

4x2+1

16 x +1

64

D)

x x –1

4x2+1

4x +1

16

Find the greatest common factor of the monomials.

76)

64x8y4 and 88x5y8

76)

A)

8x5y4

B)

704x8y8

C)

8x8y8

D)

4x3y4

Factor completely.

77)

x3– x2– 12x

77)

A)

x(x + 3)(x – 4)

B)

(x2+ 1)(x – 12)

C)

x(x + 4)(x – 3)

D)

prime

78)

x2+ 12xy + 27y2

78)

A)

(x – 9y)(x + y)

B)

(x – 9y)(x + 3y)

C)

prime

D)

(x + 9y)(x + 3y)

21

Factor by grouping.

79)

10x3– 12x2y – 25xy2+ 30y3

79)

A)

(10x2– 5y2)(x – 6y)

B)

(2x2– 5y2)(5x – 6y)

C)

(2x2+ 5y2)(5x + 6y)

D)

(2x2– 5y)(5x – 6y)

Factor completely. If unfactorable, indicate that the polynomial is prime.

80)

ab4–81a3b2

80)

A)

ab2(b +9a)(b –9a)

B)

ab2(b –9a)2

C)

prime

D)

a(b2+9ab)(b2–9ab)

81)

25t6– 1

81)

A)

prime

B)

(5t3+ 1 )2

C)

(5t3– 1 )2

D)

(5t3+ 1)(5t3– 1 )

82)

25x10 +y4

82)

A)

(5x5+y2)(5x5–y2)

B)

(5x5–y2)2

C)

prime

D)

(5x5+y2)2

22

Factor out the GCF from the polynomial.

83)

14y3–6y2+10y

83)

A)

y(14y2–6y +10)

B)

2y(7y3–3y2+5y)

C)

2(7y3–3y2+5y)

D)

2y(7y2–3y +5)

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is

prime.

84)

8z2+

6z – 9

84)

A)

(8z – 3)(z + 3)

B)

prime

C)

(4z – 3)(2z + 3)

D)

(4z + 3)(2z – 3)

Factor completely, or state that the polynomial is prime.

85)

21x2– 91x – 70

85)

A)

7(3x + 2)(x – 5)

B)

(21x + 14)(x – 5)

C)

7(3x – 2)(x + 5)

D)

prime

Write a polynomial for the length of the rectangle.

86)

?

x – 8 Area =x2– 5x – 8x + 40 square units

A)

x + 40

B)

x2– 6x – 8x + 35

C)

x2+ 8

D)

x – 5

Factor completely. If unfactorable, indicate that the polynomial is prime.

87)

x3–25x +3x2–75

87)

A)

(x –5)2(x +3)

B)

(x +5)(x –5)(x +3)

C)

prime

D)

(x2–25)(x +3)

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is

prime.

88)

4y2+

18y – 10

88)

A)

(4y – 2)(y + 5)

B)

prime

C)

2(2y – 1)(y + 5)

D)

2(2y + 1)(y – 5)

24

Factor completely. If unfactorable, indicate that the polynomial is prime.

89)

28m9– 40m6– 36m3

89)

A)

prime

B)

m3(28m6– 40m3– 36)

C)

4(7m9– 10m6– 9m3)

D)

4m3(7m6– 10m3– 9)

Factor completely, or state that the polynomial is prime.

90)

35y4+ 270y3–80y2

90)

A)

5y2(7y +2)(y –8)

B)

prime

C)

5y(7y2+2)(y –8)

D)

5y2(7y –2)(y +8)

Solve the equation.

91)

x(x + 13) = 0

A)

{–13, –1}

B)

{0, 13}

C)

{–13, 1}

D)

{–13, 0}

Find the greatest common factor of the monomials.

92)

–6x10 and 8x7

92)

A)

2x7

B)

–8x3

C)

–6x7

D)

2x10

Factor completely. If unfactorable, indicate that the polynomial is prime.

93)

x3–4x +3x2–12

93)

A)

(x –2)2(x +3)

B)

(x2–4)(x +3)

C)

(x +2)(x –2)(x +3)

D)

prime

Factor.

94)

x3– 512

94)

A)

(x – 8)(x2+ 8x + 64)

B)

(x + 512)(x + 1)(x – 1)

C)

(x + 8)(x2– 8x + 64)

D)

(x – 8)(x2+ 64)

Factor completely, or state that the polynomial is prime.

95)

x2– 4x + 4

95)

A)

(x – 2)2

B)

prime

C)

(x + 2)2

D)

(x – 2)(x + 2)

Factor completely. If unfactorable, indicate that the polynomial is prime.

96)

2x2+

4x – 48

96)

A)

2(x – 4)(x + 6)

B)

(x – 4)(2x + 12)

C)

2(x + 4)(x – 6)

D)

(–48x – 8)(x + 6)

26

Factor completely, or state that the polynomial is prime.

97)

x4–1

97)

A)

(x2–1)(x2–1)

B)

prime

C)

(x2+1)(x +1)(x –1)

D)

(x2+1)(x2+1)

Factor completely.

98)

x5+ 4x4– 45x3

98)

A)

x3(x – 5)(x + 9)

B)

x3(x – 5)(x – 9)

C)

x–5(x2+ 4x – 45)

D)

x3(x + 5)(x + 9)

Solve the problem.

99)

The width of a rectangle is 6 kilometers less than twice its length. If its area is 56 square

kilometers, find the dimensions of the rectangle.

A)

length =4 km, width =2 km

B)

length = 3 km, width =56

3 km

C)

length =7 km, width =8 km

D)

width =7 km, length =8 km

Find the greatest common factor of the monomials.

100)

16x10 and 20x6

100)

A)

16x6

B)

4x6

C)

4x10

D)

20x4