http://img165.imageshack.us/img165/8938/algos7.jpg
i get: x^2-2x-8=0
(x-4)(x+2)=0
?
http://img165.imageshack.us/img165/8938/algos7.jpg
i get: x^2-2x-8=0
(x-4)(x+2)=0
?
You need to show your working - all of it. It's impossible to see the errors you've made and the misunderstandings you most likely have.
Here're some things to consider:
f(x + 2) = (x + 2)^2 - 2(x + 2) = expand and simplify.
f(2) = 0.
Therefore f(x + 2) - f(2) = .......
Therefore $\displaystyle \frac{f(x + 2) - f(2)}{x} = \frac{........}{x} = x + 2$.
first i did:
x^2-2x(x+2) - 2x^2-4x / x
second i did:
x^3 + 2x^2- 2x^2 - 4x - 2x^2 - 4x
third i simplified and got:
x^3 - 2x^2 - 8x / x
then i divided it all by x and got:
x^2 - 2x - 8
then i set it up with 0:
x^2 - 2x - 8 = 0
finally i put it into this form:
(x-4)(x+2) = 0
sorry, but i am bewildered with what you got and how you got it. could you please show step by step how you got that?
Oh, I see. Lucky you replied.
I now know exactly what your misunderstanding is. It's a bad one. But maybe simple to fix. Read the following very carefully.
f(x+2) does NOT mean f times (x + 2), that is, f(x + 2) does NOT mean (x^2 - 2x) (x + 2) .......
If f(x) = x^2 - 2x, then I hope we can agree that f(a) = a^2 - 2a, f(b) = b^2 - 2b etc. f(apple) = (apple)^2 - 2(apple) etc. Do you see how it works? You replace the x in the rule with whatever is in ().
f(x + 2) = (x + 2)^2 - 2(x + 2). I have replaced x in the rule with (x + 2).
Then f(x + 2) = x^2 + 4x + 4 - 2x - 4 = x^2 + 2x.
Similarly, f(2) does not mean f times 2. f(2) = 2^2 - 2(2). I have replaced x in the rule with 2.
It is essential that you revise functional notation and what it means or you are in for a world of pain .....