Question

Find the GCF of 40a + 16 .(1 point)
Responses

16
16

4
4

8
8

2

Answer 1

Factor −15x − 25 using the GCF. (1 point)
Responses

​​​​​​​5(3x + 5)
5 Left Parenthesis 3 x plus 5 Right Parenthesis

​​​​​​​5(3x − 5)
5 Left Parenthesis 3 x minus 5 Right Parenthesis

​​​​​​​5(−3x + 5)
5 Left Parenthesis negative 3 x plus 5 Right Parenthesis

​​​​​​​5(−3x − 5)

Answer 2

Factor 24e + 32f using the GCF. (1 point)
Responses

​​​​​​​4(6e + 8f)
4 Left Parenthesis 6 e plus 8 f Right Parenthesis

​​​​​​​8(3e + 4f)
8 Left Parenthesis 3 e plus 4 f Right Parenthesis

​​​​​​​2(12e + 16f)
2 Left Parenthesis 12 e plus 16 f Right Parenthesis

​​​​​​​12(2e + 3f)

Answer 3

5(g+2)+3(h−4)?(1 point)
Responses

commutative property
commutative property

associative property
associative property

identity property
identity property

distributive property

Answer 4

To find the greatest common factor (GCF) of \( 40a + 16 \), we need to identify the common factors of the coefficients of the terms.

1. The coefficients are 40 and 16.
2. The prime factorization of 40 is \( 2^3 \times 5 \).
3. The prime factorization of 16 is \( 2^4 \).

Now, we identify the lowest power of common prime factors:

- The only common prime factor is \( 2 \).
- The minimum power of \( 2 \) is \( 2^3 \) (from 40).

Thus, the GCF of \( 40a + 16 \) is \( 2^3 = 8 \).

So, the answer is **8**.

Answer 5

To factor the expression \(-15x - 25\) using the greatest common factor (GCF), we first find the GCF of the coefficients:

1. The coefficients are \(-15\) and \(-25\).
2. The GCF of \(15\) and \(25\) is \(5\).

Now, we can factor out \(-5\) (since we want to factor out a negative number for a simpler representation):

\[
-15x - 25 = -5(3x + 5)
\]

Thus, the expression factored with the GCF is:

\[
-5(3x + 5)
\]

However, since we want to represent it in a way consistent with the given options, it’s equivalent to:

\[
5(-3x - 5)
\]

So the final factored form is:

\[
5(-3x - 5)
\]

Thus, the correct response is **5(−3x − 5)**.

Answer 6

To factor the expression \(24e + 32f\) using the greatest common factor (GCF), we first need to determine the GCF of the coefficients 24 and 32.

1. The prime factorization of \(24\) is \(2^3 \times 3\).
2. The prime factorization of \(32\) is \(2^5\).

The GCF is determined by taking the lowest power for each common prime factor. Here, the common factor is \(2\):

- For \(2\), the minimum power is \(2^3 = 8\).

Now, we factor out the GCF \(8\) from the expression:

\[
24e + 32f = 8(3e + 4f)
\]

Thus, the expression factored with the GCF is:

\[
8(3e + 4f).
\]

The correct response is **8(3e + 4f)**.

Answer 7

To determine which property applies to the expression \(5(g + 2) + 3(h - 4)\), let's analyze it.

1. **Distributive Property**: This property states that \(a(b + c) = ab + ac\). In the given expression, both \(5(g + 2)\) and \(3(h - 4)\) involve distributing the coefficients \(5\) and \(3\) to the terms inside the parentheses.

2. **Commutative Property**: This property allows you to change the order of addition or multiplication. It does not specifically apply to this expression as it involves distributing rather than reordering.

3. **Associative Property**: This property involves changing the grouping of numbers, e.g., \((a + b) + c = a + (b + c)\). Again, it does not directly apply here as we are not changing the grouping.

4. **Identity Property**: This property states that adding zero to a number or multiplying a number by one does not change the number (e.g., \(a + 0 = a\) or \(a \times 1 = a\)). This is not relevant to the given expression.

Since the primary action in the expression involves distributing the \(5\) and \(3\) to the terms in their respective parentheses, the correct response is:

**Distributive property.**