Title: Chapter 9 Polynomials and Factoring
Course: quiz duplicate error

Q: Find the degree of the monomial.

6x^8y^5
- 5
- 6
- 13
- 8
A: 13

Q: Match the expression with its name.
6x^3 – 9x + 3
- cubic trinomial
- quadratic binomial
- fourth-degree monomial
- not a polynomial
A: cubic trinomial

Q: Write the perimeter of the figure.
[Image]
- 9x + 7x
- 11x + 3x + 2
- 14x + 2
- 14x
A: 14x + 2

Q: Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
2 – 11x^2 – 8x + 6x^2
- –5x^2 – 8x + 2; quadratic trinomial
- 5x^2 – 8x – 2; quadratic trinomial
- –6x^2 – 8x – 2; cubic polynomial
- 6x^2 – 8x + 2; cubic trinomial
A: –5x^2 – 8x + 2; quadratic trinomial

Q: Find the degree of the monomial.

7m^6n^5
- 5
- 11
- 6
- 7
A: 11

Q: Write the polynomial in standard form.
4g – g^3 + 3g^2 – 2
- –2 + 4g + 3g^2 – g^3
- g^3 – 3g^2 + 4g – 2
- 3g^3 – g^2 + 4g – 2
- –g^3 + 3g^2 + 4g – 2
A: –g^3 + 3g^2 + 4g – 2

Q: Simplify the product using FOIL.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Find the square.

(4x – 6y^3)^2
- 16x^2 – 24xy^3 + 36y^6
- 16x^2 – 48xy^3 + 36y^6
- 16x^2 + 36y^6
- 16x^2 – 4xy^3 + 36y^6
A: 16x^2 – 48xy^3 + 36y^6

Q: Find the product.

(4p – 6)(4p + 6)
- 16p^2 – 36
- 16p^2 – 48p – 36
- 16p^2 + 48p + 36
- 16p^2 + 36
A: 16p^2 – 36

Q: Find the product.

(j + 7)(j – 7)
- j^2 + 14j – 49
- j^2 – 14j – 49
- j^2 + 14j – 49
- j^2 – 49
A: j^2 – 49

Q: Factor the expression.

w^2 + 18w + 77
- (w – 7)(w + 11)
- (w – 7)(w – 11)
- (w + 7)(w + 11)
- (w + 1)(w + 77)
A: (w + 7)(w + 11)

Q: Find the product.

(4m^2 – 5)(4m^2 + 5)
- 16m^3 – 25
- 16m^2 – 25
- 16m^4 + 25
- 16m^4 – 25
A: 16m^4 – 25

Q: Simplify the product using the distributive property.
[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Factor the polynomial.

54c^3d^4 + 9c^4d^2
- 9c^3d^2(d^2 + 6c)
- 9c^3d^2(6d^2 + c)
- 9c^4d^2(d^2 + 6)
- 9c^4d^2(6d^2 + 1)
A: 9c^3d^2(6d^2 + c)

Q: Simplify the product.

8x^2(4x^2 + 4y^6)
- 12x^4 + 12x^2y^6
- 32x^4 + 32x^2y^6
- 12x^4 + 12x^2y^6
- 32x^4 + 32xy^8
A: 32x^4 + 32x^2y^6

Q: Find the GCF of the terms of the polynomial.
8x^6 + 32x^3
- x^3
- 8x^3
- 8x^3
- 8x^6
A: 8x^3

Q: Factor the expression.

k^2 + kf – 2f^2
- (k – 2f)(k + f)
- (k + 2f)(k – f)
- (k + 2f)(k + f)
- (k – 2f)(k – f)
A: (k + 2f)(k – f)

Q: Simplify the difference.

(–7x – 5x^4 + 5) – (–7x^4 – 5 – 9x)
- 2x^4 + 2x + 8
- –14x^4 + 10x + 10
- –14x^4 – 10x + 10
- 2x^4 + 2x + 10
A: 2x^4 + 2x + 10

Q: 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?
- 6x^2 – 55x + 104 ft^2
- x^2 + 6x – 16 ft^2
- 11x^2 – 56x + 66 ft^2
- 12x^2 – 50x + 50 ft^2
A: 11x^2 – 56x + 66 ft^2

Q: Factor the polynomial.

40w^11 + 16w^6
- 8w^6(5w^5 + 2)
- 8(5w^11 + 2w^6)
- w^6(40w^5 + 16)
- 8w^5(5w^6 + 2w)
A: 8w^6(5w^5 + 2)

Q: Simplify the product.

5a^2(3a^4 + 3b)
- 8a^4 + 8ab
- 15a^8 + 3b
- 15a^6 + 15a^2b
- 8a^6 + 15a^2b
A: 15a^6 + 15a^2b

Q: Factor the expression.

x^2 – 10xy + 24y^2
- (x + 6y)(x + 4y)
- (x – 2y)(x + 12y)
- (x + 2y)(x – 12y)
- (x – 6y)(x – 4y)
A: (x – 6y)(x – 4y)

Q: Simplify the sum.
(4u^3 + 4u^2 + 2) + (6u^3 – 2u + 8)
- 10 – 2u + 4u^2 + 10^ u^3
- –2u^3 – 2u^2 + 4u – 10
- –2u^3 + 4u^2 – 2u + 10
- 10u^3 + 4u^2 – 2u + 10
A: 10u^3 + 4u^2 – 2u + 10

Q: Factor the polynomial.

[Image]
- 2x(x^2 + 2x + 4)
- 2x(x + 2)(x + 4)
- x(2x^2 + 4x + 8)
- 2x^3 + 4x^2 + 8x
A: 2x(x^2 + 2x + 4)

Q: Find the product.

(2n + 2)(2n – 2)
- 4n^2 – 4
- 4n^2 – 4n – 4
- 4n^2 + 2n – 4
- 4n^2 + 4n – 4
A: 4n^2 – 4

Q: Simplify the product using FOIL.

(3x – 7)(3x – 5)
- 9x^2 + 6x + 35
- 9x^2 + 36x + 35
- 9x^2 – 36x – 35
- 9x^2 – 36x + 35
A: 9x^2 – 36x + 35

Q: Simplify the product.

7a^3(5a^6 – 2b^3)
- 12a^9 – 9a^3b^6
- 35a^9 – 14ab^6
- 35a^9 – 14a^3b^3
- 12a^18 – 9a^3b^6
A: 35a^9 – 14a^3b^3

Q: Simplify the product.

8p(–3p^2 + 6p – 2)
- –5p^3 + 14p^2 – 6p
- 48p^2 – 16p – 24p^3
- 14p^2 – 6p – 5p^3
- –24p^3 + 48p^2 – 16p
A: –24p^3 + 48p^2 – 16p

Q: Complete.

y^2 + 15y + 56 = (y + 7)(y + [Image])
- –8
- 8
- –7
- 7
A: 8

Q: Find the area of the UNSHADED region. Write your answer in standard form.
[Image]
- –2x^2 + 10x + 25
- x^2 + 8x + 25
- 10x + 25
- x^2 + 10x + 25
A: 10x + 25

Q: Complete.

z^2 + 9z – 90 = (z – 6)(z + [Image])
- –9
- 15
- 90
- –15
A: 15

Q: Find 33^2 using mental math.
- 1,089
- 900
- 999
- 729
A: 1,089

Q: Find the square.

[Image]
- [Image]
- [Image]
- [Image]
- [Image]
A: [Image]

Q: Find the missing coefficient.
[Image] [Image] [Image]
- 65
- 5
- –5
- –65
A: –65

Q: Simplify using the vertical method.
(2k + 3)(2k^2 – 4k – 3)
- 4k^3 + 18k^2 – 2k – 9
- 4k^3 – 2k^2 + 6k – 9
- 4k^3 + 14k^2 – 6k – 9
- 4k^3 – 2k^2 – 18k – 9
A: 4k^3 – 2k^2 – 18k – 9

Q: Find the square.

(2x – 6)^2
- 4x^2 – 24x + 36
- 4x^2 – 8x + 36
- 4x^2 + 36
- 4x^2 – 12x + 36
A: 4x^2 – 24x + 36

Q: Simplify using the horizontal method.
(2n^2 + 4n + 4)(4n – 5)
- 8n^3 + 26n^2 – 36n – 20
- 8n^3 + 6n^2 – 4n – 20
- 8n^3 + 4n^2 – 6n – 20
- 8n^3 – 6n^2 + 36n – 20
A: 8n^3 + 6n^2 – 4n – 20

Q: Factor the expression.

d^2 + 10d + 9
- (d + 9)(d – 1)
- (d – 9)(d + 1)
- (d – 9)(d – 1)
- (d + 9)(d + 1)
A: (d + 9)(d + 1)

Q: Simplify the product.

3p^4(4p^4 + 7p^3 + 4p + 1)
- 12p^8 + 3p^7 + 4p^5 + p^4
- 12p^8 + 21p^7 + 12p^5 + 3p^4
- 7p^8 + 10p^7 + 7p^5 + 4p^4
- 12p^16 + 21p^12 + 15p^4
A: 12p^8 + 21p^7 + 12p^5 + 3p^4

Q: Simplify the difference.

(4w^2 – 4w – 8) – (2w^2 + 3w – 6)
- 2w^2 – 7w – 2
- 6w^2 – 1w – 14
- 2w^2 – 1w – 14
- 6w^2 + 7w + 2
A: 2w^2 – 7w – 2

Q: Simplify the product.

2n(n^2 + 3n + 4)
- 2n^3 + 6n^2 + 8n
- 2n^3 + 3n + 4
- 2n^3 + 6n + 8
- n^2 + 5n + 4
A: 2n^3 + 6n^2 + 8n

Q: Factor the expression.

36y^2 – 84y – 147
- (2y + 7)(6y – 7)
- 3(2y – 7)(6y + 7)
- (2y – 7)(18y + 21)
- 3(2y + 7)(6y + 7)
A: 3(2y – 7)(6y + 7)

Q: Factor the expression.

6x^2 + 5x + 1
- (3x – 1)(2x – 1)
- (3x + 1)(2x – 1)
- (3x – 1)(2x + 1)
- (3x + 1)(2x + 1)
A: (3x + 1)(2x + 1)

Q: Factor the expression.

x^2 – x – 42
- (x – 7)(x + 6)
- (x + 7)(x + 6)
- (x + 7)(x – 6)
- (x – 7)(x – 6)
A: (x – 7)(x + 6)

Q: Factor the expression.

3x^3 + 3x^2 + x + 1
- x(3x^2 + x + 1)
- (x + 3)(3x^2 – 1)
- 3x^2(x + 1)
- (x + 1)(3x^2 + 1)
A: (x + 1)(3x^2 + 1)

Q: Factor the expression.

15x^2 – 16xy+ 4y^2
- (3x – 2y)(5x + 2y)
- (3x – 2y)(5x – 2y)
- (3x + 2y)(5x – 2y)
- (3x + 2y)(5x + 2y)
A: (3x – 2y)(5x – 2y)

Q: Factor the expression.

[Image]
- ^ [Image]
- ^ [Image]
- ^ [Image]
- ^ [Image]
A: ^ [Image]

Q: Factor the expression.

49b^2 – 36
- (6b + 7)(6b – 7)
- (7b + 6)(7b + 6)
- (7b + 6)(7b – 6)
- (7b – 6)(7b – 6)
A: (7b + 6)(7b – 6)

Factor the following expression.
198q^3r^2 – 184q^2r^2 + 18qr^2

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 [Image] and the probability of B is [Image].

a. | Simplify [Image]
b. | What is the probability that one number cube shows 2, 3, or 4, and the other shows 1, 5, or 6?

Let a^2 – 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.

Factor the following trinomial.
w^18 – 9w^9y^5 + 14y^10

Explain how to factor the following expression.
66r^2h + 57rh + 12h

Q: Factor the expression.

4x^2 – 81y^2
- (2x + 9)(2x – 9)
- (2x + 9y)(2x – 9y)
- (2x + 9y)^2
- (2x – 9y)^2
A: (2x + 9y)(2x – 9y)

Q: Factor the expression.

k^2 – 16h^2
- (k + 4h)(k + 4h)
- (k – 4h^2)(k + 4)
- h^2(k + 4)(k – 4)
- (k + 4h)(k – 4h)
A: (k + 4h)(k – 4h)

Q: Factor the expression.

6g^2 + 11g – 35
- (3g + 5)(2g + 7)
- (3g – 5)(2g + 7)
- (3g + 5)(2g – 7)
- (3g – 5)(2g – 7)
A: (3g – 5)(2g + 7)

Q: Factor by grouping.

3x^2 + 7x – 6
- (3x – 2)(x – 3)
- (3x – 2)(x + 3)
- (x + 3)(3x + 2)
- (3x + 2)(x – 3)
A: (3x – 2)(x + 3)

Find the area of the shaded region. Show all your work.
[Image]

Factor the expression by grouping. Show your work.
24q^7 – 42q^4r + 36q^3r^2 – 63r^3

Q: Factor the expression.

[Image]
- 2(5x – 2)(2x + 3)
- 2(5x + 2)(2x – 3)
- (10x – 2)(4x + 3)
- 2(5x + 4)(2x – 3)
A: 2(5x – 2)(2x + 3)

Q: Factor the expression.

6g^3 + 8g^2 – 15g – 20
- (2g^2 – 4)(3g + 5)
- (2g^2 + 4)(3g – 5)
- (2g^2 – 5)(3g + 4)
- (2g^2 + 5)(3g – 4)
A: (2g^2 – 5)(3g + 4)

Find a pair of factors for each number by using the difference of two squares.

a. | 45
b. | 77
c. | 112

Q: Factor the expression.

50k^3 – 40k^2 + 75k – 60
- 5(2k^2 – 3)(5k + 4)
- (10k^2 – 3)(25k + 4)
- (2k^2 + 15)(5k – 20)
- 5(2k^2 + 3)(5k – 4)
A: 5(2k^2 + 3)(5k – 4)

Q: Factor the expression.

r^2 – 49
- (r – 7)(r + 7)
- (r + 7)(r + 7)
- (r – 7)(r – 7)
- (r – 7)(r + 9)
A: (r – 7)(r + 7)

Q: Factor the expression.

[Image]
- ^ [Image]
- ^ [Image]
- [Image]
- [Image]
A: ^ [Image]

Explain how to factor the following trinomial.
g^4 + 4g^2j – 60j^2

Q: Factor the expression.

16m^2 – 24mn + 9n^2
- (4m – 3n)(4m + 3n)
- (16m – 3n)(m + 3n)
- (4m – 3n)^2
- (4m + 3n)^2
A: (4m – 3n)^2

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

Q: Find the radius of a circle with an area of [Image].
- 3x – 4
- 9x – 16
- 16x + 9
- 4x + 3
A: 4x + 3

Q: Factor the expression.

16j^2 + 24j + 9
- (4j – 9)(4j + 1)
- (4j + 3)^2
- (4j + 3)(4j – 3)
- (4j – 3)^2
A: (4j + 3)^2

Q: Factor the expression.

12d^2 + 4d – 1
- (6d + 1)(2d + 1)
- (6d – 1)(2d – 1)
- (6d – 1)(2d + 1)
- (6d + 1)(2d – 1)
A: (6d – 1)(2d + 1)

Q: Factor by grouping.

a^2 + ab – 56b^2
- (a + 8b)(a + 7b)
- (a – 8)(a + 7b)
- (a + 8b)(a – 7b)
- (a – 8b)(a – 7b)
A: (a + 8b)(a – 7b)

Q: Factor the expression.

21x^2 + 55x + 14
- (3x + 7)(7x – 2)
- (3x + 7)(7x + 2)
- (3x – 7)(7x + 2)
- (3x – 7)(7x – 2)
A: (3x + 7)(7x + 2)

Q: Factor by grouping.

40p^2 – 13p – 36
- (8p + 9)(5p + 4)
- (8p – 9)(5p – 4)
- (8p – 9)(5p + 4)
- (8p + 9)(5p – 4)
A: (8p – 9)(5p + 4)

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

[Image]

Q: Factor by grouping.

21m^2 – 29m – 10
- (7m – 2)(3m – 5)
- (7m + 2)(3m + 5)
- (7m + 2)(3m – 5)
- (7m – 2)(3m + 5)
A: (7m + 2)(3m – 5)

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

Q: Find the GCF of the first two terms and the GCF of the last two terms of the polynomial.
5h^3 + 20h^2 + 4h + 16
- 5h^2, 16
- 5h^3, 4
- 5h^2, 4
- h2, h
A: 5h^2, 4

Q: Factor the expression.

48g^2 – 22gh – 15h^2
- (6g + 5h)(8g – 3h)
- (6g + 5)(8g + 3h^2)
- (6g – 5h)(8g + 3h)
- (6g – 5)(8g + 3)
A: (6g – 5h)(8g + 3h)

Q: Factor completely.
6x^4 – 9x^3 – 36x^2 + 54x
- 3x(x^2 – 6)(2x – 3)
- 3x(x^2 + 6)(2x + 3)
- 6x(x^2 – 6)(2x – 3)
- 6x(x^2 + 6)(2x + 3)
A: 3x(x^2 – 6)(2x – 3)