Chapter 8 Test

1) Factor

by grouping.

Cannot be factored

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Explanation

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2) Which is the prime factorization of 120?

The prime factorization of 120 is 2^3 * 3 * 5. This means that 120 can be expressed as the product of these prime numbers raised to their respective powers.

Explanation

The prime factorization of 120 is 2^3 * 3 * 5. This means that 120 can be expressed as the product of these prime numbers raised to their respective powers.

3) Factor

(x+1) (x+12)

(x+2) (x +6)

(x +3) (x +4)

Cannot be factored

The given expression can be factored as (x+2) (x+6). This is because each term in the expression has a common factor of x, and each pair of terms has a common factor of 2 or 6. Therefore, we can factor out these common factors to obtain the given expression.

Explanation

The given expression can be factored as (x+2) (x+6). This is because each term in the expression has a common factor of x, and each pair of terms has a common factor of 2 or 6. Therefore, we can factor out these common factors to obtain the given expression.

4) Is

completely factored? If not, what other factoring can occur?

Yes; the polynomial is completelyfactored.

No; 4 can be factored from each termof the trinomial.

No; the trinomial can be factored into two binomials.

No; 4 can be factored from each termof the trinomial AND the resultingtrinomial can be factored into twobinomials.

The given polynomial can be factored by taking out the common factor of 4 from each term of the trinomial. Therefore, the correct answer is "no; 4 can be factored from each term of the trinomial."

Explanation

The given polynomial can be factored by taking out the common factor of 4 from each term of the trinomial. Therefore, the correct answer is "no; 4 can be factored from each term of the trinomial."

5) Find the GCF of 42 and 70

7

14

196

210

The GCF (Greatest Common Factor) is the largest number that divides evenly into both 42 and 70. To find the GCF, we can list the factors of each number and find the largest one that they have in common. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The largest factor that they have in common is 14. Therefore, the GCF of 42 and 70 is 14.

Explanation

The GCF (Greatest Common Factor) is the largest number that divides evenly into both 42 and 70. To find the GCF, we can list the factors of each number and find the largest one that they have in common. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. The largest factor that they have in common is 14. Therefore, the GCF of 42 and 70 is 14.

6) Kyle is making flower arrangements for a wedding. He has 16 roses and 60 carnations. Each arrangement will have the same number of flowers, but roses and carnations will not appear in the same arrangement. If he puts the greatest possible number of flowers in each arrangement, how many arrangements can he make?

4

15

19

38

Kyle has 16 roses and 60 carnations. Since each arrangement will have the same number of flowers, the number of roses and carnations in each arrangement must be a factor of both 16 and 60. The factors of 16 are 1, 2, 4, 8, and 16, while the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The greatest possible number of flowers in each arrangement is 4, which is a factor of both 16 and 60. Therefore, Kyle can make 19 arrangements by pairing 4 roses with 4 carnations in each arrangement.

Explanation

Kyle has 16 roses and 60 carnations. Since each arrangement will have the same number of flowers, the number of roses and carnations in each arrangement must be a factor of both 16 and 60. The factors of 16 are 1, 2, 4, 8, and 16, while the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The greatest possible number of flowers in each arrangement is 4, which is a factor of both 16 and 60. Therefore, Kyle can make 19 arrangements by pairing 4 roses with 4 carnations in each arrangement.

7) Factor

(x -2) (x -8)

(x -2) (x +8)

(x +2) (x -8)

Cannot be factored

The given expression can be factored as (x + 2) (x - 8). This is because the expression consists of two binomials, one with (x + 2) and the other with (x - 8). When these binomials are multiplied together, the result is the given expression.

Explanation

The given expression can be factored as (x + 2) (x - 8). This is because the expression consists of two binomials, one with (x + 2) and the other with (x - 8). When these binomials are multiplied together, the result is the given expression.

8) Find the GCF of

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Explanation

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9) Factor 2n(n+3) -5(n+3)

( n - 3 )( 2n + 5)

(n + 3) ( 2n + 5)

( n + 3) ( 2n - 5)

Cannot be factored

The given expression can be factored as ( n + 3) ( 2n - 5) . This can be determined by using the distributive property to expand the expression and then grouping like terms together. The resulting expression can be written as a product of two binomials, where the first binomial is ( n + 3) and the second binomial is ( 2n - 5).

Explanation

The given expression can be factored as ( n + 3) ( 2n - 5) . This can be determined by using the distributive property to expand the expression and then grouping like terms together. The resulting expression can be written as a product of two binomials, where the first binomial is ( n + 3) and the second binomial is ( 2n - 5).

10)

(x + 2) (5x + 27)

(x + 3) (5x + 18)

(x + 6) (5x + 9)

Cannot be factored

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Explanation

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11) Determine whether

is a difference of two squares. If so, choose the correct factorization.

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Explanation

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12) Completely factor

Cannot be factored

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Explanation

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13) Factor

A factor is a number that divides evenly into another number without leaving a remainder. In other words, it is a divisor of a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, as these numbers can all divide 12 without leaving a remainder. Factors are important in various mathematical operations, such as finding the greatest common factor or simplifying fractions.

Explanation

A factor is a number that divides evenly into another number without leaving a remainder. In other words, it is a divisor of a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, as these numbers can all divide 12 without leaving a remainder. Factors are important in various mathematical operations, such as finding the greatest common factor or simplifying fractions.

14) Factor

(2a-7)(4a+1)

(2a-1)(4a+7)

(2a+1)(4a-7)

Cannot be factored

The given expression, (2a+1)(4a-7), is the correct answer because it represents the factored form of the given expression, (2a-7)(4a+1). By applying the distributive property, we can expand the answer to obtain the original expression. Therefore, (2a+1)(4a-7) is the correct factorization.

Explanation

The given expression, (2a+1)(4a-7), is the correct answer because it represents the factored form of the given expression, (2a-7)(4a+1). By applying the distributive property, we can expand the answer to obtain the original expression. Therefore, (2a+1)(4a-7) is the correct factorization.

15) Write the factored form of the polynomial that is modeled by this geometric diagram.

(x+3)(12x+1)

(2x+3)(6x+1)

(3x+1)(4x+3)

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Explanation

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16) Which value of b would make

factorable?

-31

-17

11

13

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Explanation

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17) Determine whether

is a difference of two squares. If so, choose the correct factorization.

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Explanation

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18) Which value of C would NOT make

factorable?

-22

-2

2

22

The value of C that would not make the expression factorable is 22. This is because for an expression to be factorable, it needs to have two factors that can be multiplied together to give the original expression. However, when C is equal to 22, it is not possible to find two factors that can be multiplied to give the expression. Therefore, 22 would not make the expression factorable.

Explanation

The value of C that would not make the expression factorable is 22. This is because for an expression to be factorable, it needs to have two factors that can be multiplied together to give the original expression. However, when C is equal to 22, it is not possible to find two factors that can be multiplied to give the expression. Therefore, 22 would not make the expression factorable.