Answer:

Sure! Let's factor each expression step by step:

1. 2x + 4 - Common monomial factoring:

In this case, we can factor out the common monomial "2" from both terms:

2(x + 2)

2. 2x + 8:

There is no common monomial to factor in this expression, so it remains as it is.

3. x^2 + 5x + 6 - Quadratic trinomial factoring:

To factor this quadratic trinomial, we need to find two numbers whose product is 6 and whose sum is 5. The numbers are 2 and 3.

Therefore, we can factor it as:

(x + 2)(x + 3)

4. 3x + 15 - Common monomial factoring:

We can factor out the common monomial "3" from both terms:

3(x + 5)

5. -x^2 - 4 - Difference of Two Squares:

This expression is in the form of a difference of squares, where -x^2 can be considered as (-1)(x^2) and 4 as (2^2).

Therefore, it can be factored as:

-(x + 2)(x - 2)

6. x^2 - 16 - Difference of Two Squares:

This is also a difference of squares expression, where x^2 can be considered as (x^2) and 16 as (4^2).

Therefore, it can be factored as:

(x + 4)(x - 4)

7. x^2 + 8x + 16 - Perfect square trinomial:

This is a perfect square trinomial. It can be factored as the square of a binomial:

(x + 4)^2

8. 3x + 18 - Common monomial factoring:

We can factor out the common monomial "3" from both terms:

3(x + 6)

9. x^2 + 7x + 10 - Quadratic trinomial factoring:

To factor this quadratic trinomial, we need to find two numbers whose product is 10 and whose sum is 7. The numbers are 2 and 5.

Therefore, we can factor it as:

(x + 2)(x + 5)

10. x^2 - 25 - Difference of Two Squares:

This is a difference of squares expression, where x^2 can be considered as (x^2) and 25 as (5^2).

Therefore, it can be factored as:

(x + 5)(x - 5)

Final answers:

1. 2(x + 2)

2. 2x + 8

3. (x + 2)(x + 3)

4. 3(x + 5)

5. -(x + 2)(x - 2)

6. (x + 4)(x - 4)

7. (x + 4)^2

8. 3(x + 6)

9. (x + 2)(x + 5)

10. (x + 5)(x - 5)