If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?  Pick one
A) 8 B) 2 C) − 2 D) − 3 E) − 5
Given: x^2 − 2x − 15 = (x + r)( x + s)   Factor to get: (x - 5)(x + 3) = (x + r)( x + s)   Rewrite as: (x + -5)(x + 3) = (x + r)( x + s)   So, it's possible that r = -5 and s = 3   Here, r - s = (-5) - 3   = -8   Try REVERSING the factorization:   x^2 − 2x − 15 = (x + r)( x + s)   Factor to get: (x + 3)(x - 5) = (x + r)( x + s)   Rewrite as: (x + 3)(x + -5) = (x + r)( x + s)   So, it's possible that r = 3 and s = -5   Here, r - s = 3 - (-5)= 
<gadget id="calculator">3 - (-5)</gadget>
<output>8</output>
8   8nswer: 8
<result>A</result>
If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?