Could somebody help me with factoring completely?....

Question

anonymous · Answer

x^3-2x^2+x-2

hartnn · Answer

factor out x^2 from 1st 2 terms,
what do u get ?

anonymous · Answer

I don't understand how to do any of this.

hartnn · Answer

$x^3 = x\times x \times  \ 2x^2 = 2\times x\times x$
so, the common terms are x and x, which is x^2 
from $x^3$, one x remains, and from $2x^2$, only 2 remains,

so,
$x^3-2x^2 = x^2 (x-2)$

hartnn · Answer

does that make sense ?

anonymous · Answer

It kinda makes since to me... I mean I get what you did and how I just don't feel I could figure that out hah...

hartnn · Answer

practice it few times, and it will become easy for you!

so we have 
$x^2(x-2)+1(x-2)$
factoring out x-2, we get 
$(x-2)(x^2+1)$
got this ? you understand factoring, right ?

anonymous · Answer

I do understand this.. 
so it would be, 
x^3+x-2x^2-2

hartnn · Answer

that was your question....
and we factored it as (x-2)(x^2+1)
ask if any doubt in any step...

anonymous · Answer

It says the correct answer is (x-2)(x+i)(x-i)...

hartnn · Answer

oh the topic was Complex numbers ?? then we needed to  further factor x^2 +1 
which actually comes out to be (x+i)(x-i)

anonymous · Answer

Could you help me with 
x^3+x^2-x-3 then?