How would I factor equations like this? x^2 + 3x + 2. or x^2 - 2x - 15thank you

There are two  quadratic expressions
given.

x^2+3x+2 and  x^2-2x-15. To find the
factors.

1)

To find the
factors of x^2+3x+2, we split the middle term 3x  into two terms in sich a way that the 
product of the two split terms equal to the first and last
term.

3x  is split into two terems 2x + x. Product of the
split terms = 2x*x = 2x^2. Product of the 1st and last terms = x^2 * 2 =
2x^2.

Now group the terms and find the common factors
(CF) for each
group.

 (x^2+2x)+(x+2).

x(x+2)
+1(x+2). x+2 is the CF.

Take out the
CF:

(x+2)(x+1).

2)

x^2-2x-15.

-2x
= (-5x)+(3x). And (-5x)*(3x) = x^2*(-15).

Therefore
x^2-2x-15 = (x^2 -5x)+(3x-15) = x(x-5)+3(x-5) =
(x-5)(x+3).

x^2-2x-15 = (x-5)(x+1).