SOLUTION: I really someone to show me step by step how to solve this one....and if possibly explain it to me.....that will be awsome... Directions: Find all positive values for k for whic

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 72339: I really someone to show me step by step how to solve this one....and if possibly explain it to me.....that will be awsome...
Directions: Find all positive values for k for which each of the following can be factored.
x^2+x-k
Found 2 solutions by pradhyumna.kumar@gmail.com, jim_thompson5910:
Answer by pradhyumna.kumar@gmail.com(62) (Show Source):
You can put this solution on YOUR website!
Find all positive values for k for which each of the following can be factored.
x^2+x-k
for all the values of k > (1/4)

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
You're looking for a number which allows you to find 2 numbers that add to 1. There are infinite possibilities for this to happen. For instance you could have k=30 and the polynomial could factor to (x+6)(x-5) (which FOILs to x^2+x-30). Or you could have k=42 and the polynomial factors to (x+7)(x-6) (which FOILs to x^2+x-42). The list of k values is infinite, but k needs to be the product of 2 factors which have a difference of 1 (for instance 6 and 7, or 5 and 6) in order for this to work.