SOLUTION: One way to factor a trinomial such as x^2 - 8x - 3 is to assign a value such as 10 to and evaluate the expression. Try the above method to factor x^2 - 8x + 15. Show your work

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: One way to factor a trinomial such as x^2 - 8x - 3 is to assign a value such as 10 to and evaluate the expression. Try the above method to factor x^2 - 8x + 15. Show your work       Log On


   

Question 1026308: One way to factor a trinomial such as x^2 - 8x - 3 is to assign a value such as 10 to and evaluate the expression.
Try the above method to factor x^2 - 8x + 15. Show your work and explain each step did the method give you the correct factors?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry but  x² - 8x - 3 does not factor.

Did you copy it wrong?

However  x² - 8x + 15 does factor.

We assume it factors as (x-a)(x-b), so
then: 

 x² - 8x + 15 = (x-a)(x-b), 

Substitute x=10

10² - 8∙10 + 15 = (10-a)(10-b)
      100-80+15 = (10-a)(10-b)
             35 = (10-a)(10-b)

35 factors as 7∙3 so

So we set 10-a = 7 and 10-b = 5

That gives:

a = 3 and b = 5

So  (x-a)(x-b) becomes (x-3)(x-5)

Edwin