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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
In order for r%5E2-2r%2Bk+ 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 12%2Bq=-2 and solve for "q" to get q=-2-12=-14


So the numbers 12 and -14 add to -2. They multiply to %2812%29%28-14%29=-168


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 k=-168, then the polynomial r%5E2-2r-168 can be factored and it factors to %28r%2B12%29%28r-14%29


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