Question 203803: Hi again, I was wondering if someone could show me how to do the following;
Factorize 6x^2 + x - 12.
and Expand (x + 1)(-2x + 1)(x - 3).
Both are seperate equations and I need different answers. If someone could show me how to do them that would be great.
Thanks, -Nick
Answer by PRMath(133)   (Show Source):
You can put this solution on YOUR website! Hi Nick....
Before we start... have you had much work with factoring? I will give you a small example, just to be sure of what you understand, k?
For example... say you had:  What you have to say to yourself is: What would we use to MULTIPLY to get to 16 and yet ADD to get to 8. Well, a pretty typical way to get to 16 is to multiply  but... I can't see any way to add those up to get to 8. Can you? Nope, probably not.
How about  ? That would multiply to be 16 and yet add to be 8. So we'd put that info into an equation like this;
 THEN if we use FOIL, we can see that we will indeed come up with our original equation of . I'm assuming you know FOIL but if not, repost and I'll explain further.
SO now that we have reviewed factoring a TINY bit, let's look at your original equation:  .
In this case, you have to get numbers that MULTIPLY to get to -12, YET they must ADD up to be +1. There is a +1 in front of the "x" --- think of this:
BUT we have a 6 at the front of our equation. That makes things harder because you have to choose first terms that multiply to be 6. Sooo what you can do is sort of test some ideas..........
 . OH no. That won't work at all. We get -12 for multiplying but using FOIL, we get -18x + 4x. That would give us -14x. ARghhhhhhhhhh. That's no good.
HOW about......
What can we multiply to get 12? How about 3 times 4? Let's plug that in.....
 Could this be the factoring? Let's check this with FOIL
First:  GOOD
Outside:  Ok.....
Inside:  Ok.....
Last:  GOOD.
So we ended up with: 
Combine like terms:
OH so we have our equation. Therefore we know that our factoring is correct. Yay.
Now to expand.................
(x + 1)(-2x + 1)(x - 3)
Let's just focus on the last two parts of the equation: (-2x + 1)(x - 3)
Let's use FOIL on that:
First: 
Outside: 
Inside: 
Last: 
That gives us: 
Combine like terms: 
BUT we are not done. Don't forget we have another part of the equation... We still have to multiply by (x + 1)
SO we mutiply like this: 
We take the "x" in (x + 1) and multiply it by EVERYTHING, like this:
Sooo now we have:  BUT we are STILL not done...
We have to take the 1 in (x+ 1) and muiltiply it by EVERTHING, too!
Sooo now we have:
We are STILL not done (and this would be SO much easier to show you in person. Typing it all out is going to confuse you further, I'm afraid but here goes)...
 Now combine like terms......
THAT is your final answer. Whewwwwwwww.
I hope this helps but my guess is that it will be very confusing.... sigh.
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