What is a factor of 4x^2 + 36x + 72

Question

anonymous · Answer

Could someone explain step by step how to do this?

ness9630 · Answer

Start off by factoring out a 4.

anonymous · Answer

This leaves x^2 + 9x + 18

anonymous · Answer

Well 4(x^2 + 9x + 18)

ness9630 · Answer

Correct, now factor what's inside, and to be correct it'd be
$$\LARGE 4(x^2+9x+18)=0$$

anonymous · Answer

(x + 3)(x+6)?

anonymous · Answer

But the problem is none of that looks like the answer

anonymous · Answer

Well, the given answers

ness9630 · Answer

We're not finished:
Now divide everything by 4 to leave:
(x+3)(x+6)=0
Now solve separately:
x+3=0
x+6=0

anonymous · Answer

Oh. Wow. Thanks :)

So, x = - 3 and x = -6

anonymous · Answer

But there should be only one answer? So I'm guessing I did something wrong.

ness9630 · Answer

Correct, and you're welcome 
$$\Huge\color{green}{\ddot\smile}$$

ness9630 · Answer

What are your answer choices?

anonymous · Answer

One of them is x -6, so I'm guessing that is it :) It only ask for one factor.

anonymous · Answer

THANK YOU :)

ness9630 · Answer

That's strange, there should be two solutions..

anonymous · Answer

Yeah, it sometimes has errors.

anonymous · Answer

COuld you help me with this one? What is a factor of x^2 - 6x -27

anonymous · Answer

Wouldn't it be (x-9)(x+3)

ness9630 · Answer

Yup!

anonymous · Answer

But it doesn't list it

anonymous · Answer

x + 3 

 x + 9 

 x − 1

anonymous · Answer

And it does have None of the Above, but could it be x +3? Since that is a factor of it...?

ness9630 · Answer

When factoring, you usually have TWO solutions. I know for a fact that both problems we did had two solutions. 
I would pick "None of The Above."

ness9630 · Answer

Unless there was a mistake with the answer choices.

anonymous · Answer

It is just asking for one factor. Could that be it?

ness9630 · Answer

Oh, one factor. That clears everything up.. so yes.

anonymous · Answer

Ha ha, sorry, my mistake

ness9630 · Answer

You can always check your solution too, by using synthetic division.

anonymous · Answer

What about this one: 48x^2 - 26x + 3? It doesn't have any factors?

anonymous · Answer

I haven't learned synthetic division yet

ness9630 · Answer

It's pretty simple, it's like upside down division.

ness9630 · Answer

Here, as an example we will use the previous problem:
|dw:1381723224558:dw|