Complex Equations? factoring 4x^2 + 14x + 6

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xwintersnight

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Nov 12, 2007
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18
I think that's what they're called. Sorry if I'm wrong =(

So, there's this huge worksheet that I've been working on pretty much the entire week. I still don't really get it, and my math teacher isn't going to be at school on Monday. Right now, I'm trying to finish the section that tells you to factor the expressions.

How do you factor the following equation?

4x[sup:sw6geu8y]2[/sup:sw6geu8y]+14x+6

I can factor 2x[sup:sw6geu8y]2[/sup:sw6geu8y]+4x+2, but everything is all even in that equation, and everything fits within each other. So, these new number combinations really confuse me. Can you please help me?

--Meadow
 
Re: Complex Equations???

Well first off, you can see that you can factor out a 2 of the expression so it could be a bit more easier to deal with:
4x[sup:2idq5nng]2[/sup:2idq5nng] + 14x + 6
= 2(2x[sup:2idq5nng]2[/sup:2idq5nng] + 7x + 3)

Here's an example that goes through the steps of factoring "complex" quadratics:
http://www.purplemath.com/modules/factquad2.htm

Come back if you still have any problems :wink:
 
Re: Complex Equations???

hey, i'm new. did you figure it out yet? i know a sort of long process that ALWAYS produces the right answer, if you don't have it yet.
 
Re: Complex Equations???

cjswonderfulgirl: No, I haven't figured it out yet. I know someone will eventually come along and be able to help me understand, because it hasn't failed in the past.

jwpaine: Thanks, John. It seems to be making sense so far... =)
 
Re: Complex Equations???

4x^2+14x+6
i wasn't talking about that. if you multiply the first and last terms, you will get 24. then, make a list of the factors of 24:6,4 12,2 and so forth
12 and 2 will work, so use those to add together to make 14x
so, your new equation will be 4x^2 +12x+2x+6.
then you can use facoring by grouping:
(4x^2 +12x)+(2x+6)
then, factor out what you can
4x(x+3)+2(x+3)
which will make
(4x+2)(x+3)
hope you understand and you're not just looking for answers:)
 
Re: Complex Equations???

That sort of makes sense. I'm obviously not just looking for answers. I'm trying to actually understand the principles so that I can apply them to the 23 other similar problems.
 
Re: Complex Equations???

well, whatever's easiest for you. i like to learn that method (i learned it in 9th grade and have been using it ever since). it sticks to some people.
 
Re: Complex Equations???

The grouping method is good: it's how most other methods are derived... and there really aren't other methods besides rational roots tests + polynomial division, grouping method and constructing binomial factors from completing the square...... it's often best just to use the grouping method unless your quadratic doesn't have rational roots.
 
Re: Complex Equations???

So, let me see if I really get this...

The Problem
6x[sup:z6k12620]2[/sup:z6k12620]-33x+15

Product of ac
(6)15=90

Factoring
90< 30 and 3

(30)3=90 and 30+3=33

Re-write
So, then I re-write the equation as 6x[sup:z6k12620]2[/sup:z6k12620]-30x-3x+15.

Grouping
(6x[sup:z6k12620]2[/sup:z6k12620]-30x)+(-3x+15)

2x(3x-15)+(-3x+15)

Simplify
... okay, I'm stuck now. How would I simplify this now (if I've even done it correctly so far)?
 
Re: Complex Equations???

\(\displaystyle 6x^2- 30x - 3x + 15\)
\(\displaystyle (6x^2-30x) - (3x + 15)\)
\(\displaystyle 6x(x + 5) - 3(x + 5)\)

Now factor once more
 
Re: Complex Equations???

Did you get it? What's the common term in 6x(x + 5) and -3(x+5) that you can factor out?
 
Re: Complex Equations???

Yep. Good job :wink: That's exactly what factoring is!

You could also further factor out a 3 from that last binomial.
 
Re: Complex Equations???

o_O said:
How about the (x+5)?
Click to expand...
xwintersnight said:
Do we just take that part out, then, and make it (x+5)(6x-3)?
Click to expand...
Incorrect!

\(\displaystyle 6x^2 - 30x - 3x + 15\)
\(\displaystyle 6x(x - 5) - 3(x - 5)\)
\(\displaystyle (x - 5)(6x - 3)\)

Which expands back into: \(\displaystyle 6x^2 - 33x + 15\), where your solution expanded into: \(\displaystyle 6x^2 + 27x - 15\)
 
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