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Mathematics 8 Online
EndersWorld:

Help me ;~;

EndersWorld:

\[\frac{ 2x^2-6x-8 }{ x^2-1 }\]

EndersWorld:

I’m really confused.

Hero:

Ah I see. So with these, you factor one at a time. Let's start with \(2x^2 - 6x - 8\)

Hero:

With this one, you have to look to see what is common to each factor first and then factor that out. Do you see?

EndersWorld:

1 attachment
EndersWorld:

ac I have set a \[-4\] BTW

Hero:

What we're trying to do is figure out what factor is common to the 2, 6, and 8. Only one number is common to each.

EndersWorld:

2

Hero:

Very good, so you'll have to factor that out first.

EndersWorld:

I divided instead of subtracting.. I’m a idiot e.e

EndersWorld:

a=1 b=-4 c=-6 ac=-6

Hero:

Well .... actually, when you factor out a number you do DIVIDE.

EndersWorld:

...

Hero:

You divide the coefficient of each term by 2

EndersWorld:

a=1 b=-3 c=-4 ac=-4

Hero:

Here's how to write it when you have factored out the 2: \(2(x^2 - 3x - 4)\) But what you have written above is correct. We still now need to factor \(x^2 - 3x - 4\)

EndersWorld:

Check chat..

EndersWorld:

I know my numbers are -4 and 1 -4+1=-3 -4*1=-4

Hero:

Very good.

EndersWorld:

\[x^2-(4+1)-4\]

Hero:

don't forget the x after the parentheses

EndersWorld:

Ima kill myself *^* \[x^2-(4+1)x-4\]

Hero:

Very good. So you know what to do next :D

EndersWorld:

Distribution. :0

EndersWorld:

\[x^2+4x-1x-4\]

Hero:

Very good. Now there are two ways to proceed from here. You could go ahead and factor by grouping which is what I would rather you do at this point. Go ahead and try.

EndersWorld:

x(4)-(x+4)

Hero:

Remember, if you have factored correctly, what remains in parenthesis are two binomials that will be the same expression.

EndersWorld:

x(4)- x(4)

Hero:

Well, just to clarify, what you wrote the first time was almost correct. Now it is way off.

EndersWorld:

I will be back on tomorrow morning or so, roughly in 12 hours, I gotta do dishes and shower, sorry to cut it short, thank you so much!

EndersWorld:

Great...

Hero:

Good luck.

EndersWorld:

Okay... so I screwed it up.

EndersWorld:

x(4)-(x+4)

Hero:

But that's the same thing you wrote 9 replies ago.

EndersWorld:

Yep, reposted so I could try and find a different way to make it correct.

Hero:

Just look back at the previous step before that step and think logically about what you are actually factoring out and what should remain afterwards.

EndersWorld:

(x+4)(x+4)

Hero:

Well ... I know. It's a bit confusing for you, but you were supposed to factor out x from the first two terms and factor out -1 from the last two terms doing so, you would have this: x(x+4) - 1(x + 4)

EndersWorld:

You’re right, that is very confusing.

Hero:

Now you should be able to finish from there.

Hero:

Well, let me do some tricks to help you understand better.

Hero:

\(\color\red{x}^2+4\color\red{x}\color\green{-}x\color\green{-}4\)

Hero:

Hopefully you can see red and green to highlight what is common to each pair of binomial terms

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