SOLUTION: Find two negative values of "k" for which the given polynomial can be factored. (there may be many possible values) Page 219, problem 39 r^2-2r+k thank you very much f

Question 201872: Find two negative values of "k" for which the given polynomial can be factored. (there may be many possible values)
Page 219, problem 39
r^2-2r+k

thank you very much for your help
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order for to be factored, there must be two whole numbers that multiply to "k" AND add to -2.

So let's pick a random number. I'm going to pick 12. Now what number must I add to 12 to get -2? Well, we can set up the equation and solve for "q" to get

So the numbers 12 and -14 add to -2. They multiply to

So it turns out that the two numbers 12 and -14 both add to -2 (the middle coefficient) AND multiply to -168. So if we let , then the polynomial can be factored and it factors to

I'll let you find another value of "k". Simply use the logic used above to find another "k" value.
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