SOLUTION: HELP PLEASE...Find all positive values for k for which each of the following can be factored: x^2+x-k

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: HELP PLEASE...Find all positive values for k for which each of the following can be factored: x^2+x-k      Log On


   

Question 83643: HELP PLEASE...Find all positive values for k for which each of the following can be factored:
x^2+x-k
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
this expression is factorable as long as the difference in the factors of k is 1

x^2+x-6=(x+3)(x-2) ... x^2+x-132=(x+12)(x-11) ... etc.

so k=(n+1)n for n>=0 ... where n is an integer value

the negative value of k in the expression means one of the factors is negative, giving the x term a coefficient of 1