Question

Factor the following polynomial

x^3 + 3x^2 + 4x + 12

Help me with the steps and explain

Answer 1

Begin with the "factor by grouping" method.

Do you know how to do this?

Answer 2

Yes

Answer 3

Good. So you factor the polynomial into:

(x^3+3x^2) + (4x+12)

Now you need to find the common numbers and variables in each parenthesis set, or in other words, factor the binomials. What can you take out and put in front from (x^3+3x^2) and (4x+12).

Answer 4

That part confuses me.... But I just want you to teach it too me

Answer 5

Ok! :)

You need to find common numbers and variables from the binomials.

Let me explain to you with an example problem, and if youre still having trouble we can focus on your question.

Our example problem will be this: (5x^3+35x^2) + (2x+14)

I am now going to look for commons in the first binomial; (5x^3+35x^2). I see that there is a common number: \[5\] (5 goes into 5 and 35) and x^2. Therefore you take out 5x^2. It becomes 5x^2(x+7)

(5 goes into 35 seven times which is where the seven come from.)

Now we focus on the next, more simple looking, binomial; (2x+14) I see that there is only a numeric common, which is two. I will take this information and it will become 2(x+7). Note that (x+7) is common in both of these binomials and will be a part of your final answer.

To complete the equation, I pull the numbers from outside the parenthesis, which was 5x^2 and 2 and put them together (5x^2+2) and then finally we add the common binomial from both of these which was (x+7).

(5x^3+35x^2) + (2x+14) factors into (5x^2)(x+7).

Answer 6

It factors into (5x^2+2)(x+7).

I made a typo in the original explanation answer.

Do you understand this?

Answer 7

So after i factor I pick a formula???

Answer 8

And I factor the equation is this the x(x+3) + 4(x+3)

Answer 9

Sorry I am talking about my own equation I wanted to show you if I was understanding it !!!

Answer 10

You are getting close.

(x^3+3x^2) + (4x+12)

In (x^3+3x^2) I see that I can take out only x^2, therefore it becomes x^2(x+3).

In (4x+12) I see I can take out only 4, so it becomes 4(x+3)

Answer 11

Ok please keep explaining this is helpful.... Know what's next !!

Answer 12

:)

We are on the final step of figuring out this polynomial. It is very simple.

So, we have factored it down to \[x^{2}(x+3) + 4(x+3)\]

To SOLVE this problem, we will first make sure there is a common number within the parenthesis, and there is (x+3). This will be a part of your final solution. Once you have that, you group together the numbers/variables outside of the parenthesis. In this case it is x^2 and 4.

Therefore the final solution is \[(x^{2}+4)(x+3)\]

Answer 13

Ok that answer is correct here the thing I don't know if you would like to keep helping me out I have four more equations??? It ok if you say no

Answer 14

Open a new thread with another equation and I will attempt to help you. I am also studying for a philosophy exam on Wednesday. Do you understand the basic principles of this?

Answer 15

Ok! That's fine I'll let you study