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How to factor this?

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1 Answer

There are probably a few ways to go about a problem such as this, but the first thing that came to my mind was group factoring.

Step One:
The first thing to always do with factoring is looking for like terms. You can see that the first two terms share an x whereas the second have nothing in common.

x^2+xi-i-x

Step Two:
Factor the first set and examine what's left.

x(x+i)-i-x

Step Three:
You can notice the i and x are common, but the sign is different. Thus, I factor out the negative one on the right grouping.

x(x+i)-(i+x)

Step Four:
Now you can see that there is another common factor. (x+i) is equal to (i+x) which means it can also be factored out to leave you with: 

(x+i)(x-1)

If you do the multiplication, it should multiply out as well to check your answer.
 
I hope this was helpful.