If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which...
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?
Answer/Solution
8
Steps/Work
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)
= 8
Answer: A
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)
= 8
Answer: A