Which of the following represents the factorization of the polynomial below

The answer is D. (2x+1)(x+5) because:

I'm not sure if you've ever heard of this method of factoring and I doubt you've had considering one of my teachers and his colleagues invented it, but it's a very effective easy method to use when factoring. It takes some time to get used to, but once you understand it you can solve many problems easily. It's also not a method that you'll find on the internet and no one else out there really knows about it, so if you try to look it up later on the internet odds are you won't find it. So if you're interested in learning it, this will be your only chance. Also, I don't know if your teachers uses this method or allows it, so just know that it's one way to solve the problem and it may not be the way your teacher wants it to be solved.

Sorry that was long anyway let me explain:

You would multiply the c by the a to get 10 (c=5 and a=2, just in case you didn't know that's what those numbers are called in the formula)

So then you set up the problem as 10 on top and 11 (b) underneath, leaving a space in between for two numbers to fit. Then you ask yourself what multiplies to get 10 and adds to get 11. The answer is 10 and 1.

Step 1:

10
---

---
11

Step 2:

10
---
10
1
---
11

Step 3:

After this you look at the a (2) and ask yourself what two factors are also factors of these two numbers. In this case, the only factors are 2 and 1, which work for this problem because 2 and 1 are factors for each one of the number (10 and 11). 2 is a factor of 10 so you would divide it by 10 and 1 is a factor of 1, so you divide that by 1.

10
---
10/2=5
1/1=1
---
11

Step 4:
Now all you have to do is list them. Alright so, the number on the top left (2) is placed in front of the x (it becomes the coefficient of x). Therefore it is 2x and you look across it (diagonally) to the 1, which becomes the second part of the equation. Then you go to the bottom left and the 1 becomes the coefficient of x and diagonal from that is a 5. Hence, the two factors becoming (2x+1)(x+5). So D is the answer.

I know you are probably thinking it's a long and complicated method, but it's actually pretty easy and simple to do once you get the hang of it.