Algebra
posted by TOM on .
I have a question I hope someone can explain it to me.
We are working on Demonstrate that f actoring a polynomial. I was ask Why can you factor x²  4 but you cannot factor x² + 4? How can you tell quickly which ones you can factor and which you cannot? I am not sure what to answer here. I feel like it has some thing to do with the GCF but I am sure can some just give me an example and explain to me.

actually, one can factor x^2 + 4
(x+2i)(x2i) are the factors, where i is the sqrt of 1.
The reality is that you cant look at a polynomial and know how many real factors there are. Experience helps, but when one has
x^3+3x^23x14 there is no easy way to know without some detailed examination. 
The X^2  4 can be factored because the negative sign allows us to make one factor + and the other one  as in
(x+2)(x2) which when we expand it has the middle term cancelto wit:x^2 +2x2x4.
When we try to factor x^2+4, we KNOW both factors must be EITHER + or  because + x + = + and  x  = +. As long as the two factors have the same sign, we always get a middle term BUT x^2+4 has no middle term. 
So if I understanding this for example I have x^26 I can factor because the negative sign I can get a middle term
which would be
(x+2)(x3) expand it to
(x^2 +2x3x6)
(x^(2)x6)
With x^2+6 I could not get a middle term because the sign is positive which shows me that because When you multiply two + togther you a + and when you mulitiply two  togther you get a + so this can not have a middle term
Did I understand this correct