I'm stuck on these math problems could someone plz help?

Question

Could someone please help me with these math problems.. Thank you so much

1. Factor
x^2 + 10x + 16

2.Factor
2y^2 - 32

A) 2(y – 4)(y + 4)
B) 2(y + 4)(y – 8)
C) 2(y + 16)
D) prime

3. Factor:
x^2 + 13x + 42
What is one of the factors?

A) (x + 6)
B) (x – 7)
C) (x – 6)
D) prime

Answer 1

1. (x + 8)(x + 2)
2. A) 2y(y - 4)(y + 4)
3. A) (x + 6)

Answer 2

1. The coefficient of the first term is 1 and both signs are positive, so the form of the factors must look like (x + ?) (x + ?)

Do you see that?

Now you must find two numbers that when multiplied yield 16 and when added yield 10. You could specifically solve for the numbers using simultaneous equations. But this problem is simple enough that you should be able to guess the factors.

2. Simplify first by dividing through by 2. Now you need to factor y^2 - 16. Any binomial of the form x^2 - C can be factored as (x + sqrt(C) ) (x - sqrt(C) ). Memorize that.

3. This is of the same for as the first so you can factor it the same way. This question can actually be answered without doing the factoring though. As I noted in the first problem, the signs are both positive, so the factors must be (x + ?)(x + ?). In the supplied answers only one answer is possible (prime is not a valid option)

Answer 3

1)(x+2)(x+8)
2)2(y – 4)(y + 4)
3)(x + 6)