There are two quadratic expressions given.
x^2+3x+2 and x^2-2x-15. To find the factors.
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(x+2) +1(x+2). x+2 is the CF.
Take out the CF:
-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).