



 
Hi Ema, Your first question involves a common factor. Let's look at a similar question.
What you need to recognize is the x in both terms, in fact x^{2} = x x so you might see this expression as
You can take one x out as a common factor so
You can't factor this any further so this is the expression in a completely factored form. Common factors can be more complex than in my first example. Let's try
Here I see (x + 2) as a common factor so
but I'm not done since 2x^{2}  4 has a common factor of 2 so
Now I'm done. For your second problem x^{2} + 2x + 3 if it factors the factorization will look like
where a and b are some numbers. If you expand the right side you get x^{2}, two terms that contain x and ab. Hence, if my factoring was successful ab = 3. Thus a and b be 1 and 3 or and and b must be 1 and 3. Hence the factored form would have to be
Expand both of these. Do you get x^{2} + 2x + 3 in either case? If so then you have a factorization, if not then x^{2} + 2x + 3 doesn't factor. I hope this helps,  


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