Random thing I was thinking about.
For example, when solving quadratics for example, I equal it to 0.

x^2+2x-8=0
You can take out a factor of (x+4) to get (x+4)(x-2)=0. Then you can equate them both to 0 to get the answer.

What I want to know is what is stopping me from taking out a random factor i.e. (x+7)
(x+7)((x^2+2x-8)/(x+7))=0 And then getting x=-7.

That's a simplified analogy and I know you wouldn't do it, but it gets more complicated when taking things out in trig.

Question

Random thing I was thinking about.
For example, when solving quadratics for example, I equal it to 0.

x^2+2x-8=0
You can take out a factor of (x+4) to get (x+4)(x-2)=0. Then you can equate them both to 0 to get the answer. 

What I want to know is what is stopping me from taking out a random factor i.e. (x+7)
(x+7)((x^2+2x-8)/(x+7))=0 And then getting x=-7.

That's a simplified analogy and I know you wouldn't do it, but it gets more complicated when taking things out in trig.

anonymous · Answer

Naw, not really. I mean it's zero. Either way it doesn't really matter.

henryblah · Answer

? I'm not understanding what you mean.

cwrw238 · Answer

x+ 7  / x + 7 = 0/0 if x = -7.     0/0 is meaningless

kinggeorge · Answer

In essence, if you do that, you'll be dividing by 0. And you can't do that.

anonymous · Answer

@cwrw238 said what I was trying to say. :)

henryblah · Answer

Ok. So if I had 4(cosx)^2-2-sinx-cosx=0
Could I divide by cosx and equate that to 0?
i.e. cosx(4cosx)-2secx-tanx-1=0

henryblah · Answer

Whoops cosx(4cosx-2secx-tanx-1)=0
Brackets over entire thing

kinggeorge · Answer

I don't think that would work.

henryblah · Answer

Is there a reason why -.-?