## anonymous one year ago Okay, really struggling on this one :/ I just need hep finishing the problem. x-1/(5x^2 - 8x +3) times 4(5x - 3)/x-11

1. anonymous

@zepdrix Let me know if I'm annoying you at anytime!!

2. anonymous

3. zepdrix

4. zepdrix

What's going on? Factoring stuff and simplify again?

5. anonymous

Well, I'm just stuck here :/ I can't find a way to further factor it! I already factored a simplified some of it.

6. zepdrix

Oh it's one of these types :O

7. anonymous

Uh-oh, that doesnt sound good ;(

8. zepdrix

|dw:1440828539698:dw|Have you learned this goofy method before?

9. anonymous

Not at all!?

10. zepdrix

Ehhh scratch that, let's do factor by GROUPING instead :) That's a better approach anyway.

11. anonymous

Ohh I know how to do that ;p But I thought you needed 4 terms?

12. zepdrix

Hmm :d no. You start with 3 terms, and yes, you'll break them into 4 terms in order to do your grouping.

13. zepdrix

So what you're doing is, splitting the middle term in some clever way so you can have nice groups.

14. zepdrix

$\large\rm 5x^2\color{orangered}{-8x}+3$

15. anonymous

Okay, then I haven't done this before haha. Uhmm I really have no idea :/

16. zepdrix

We'll multiply A and C, giving us 15. Factors of 15 that add to -8? Hmm

17. zepdrix

15*1 = 15 15 + 1 = 16 Hmm those didn't work

18. anonymous

5 and 3

19. zepdrix

5 * 3 = 15 5 + 3 = 8 Hmm it didn't give us -8 though D:

20. anonymous

;( I have no clue how to get -8 from the factors of 15..

21. anonymous

Oh!!! Lol why do I always miss this?? -5 and -3! lol

22. zepdrix

Ok good. So that's telling us that we want to rewrite -8x as -5x and -3x.

23. zepdrix

$\large\rm 5x^2\color{orangered}{-8x}+3$$\large\rm 5x^2\color{orangered}{-5x-3x}+3$

24. anonymous

Ohh okay I remember this! And the groups are (5x^2 - 5x) and (-3x +3)

25. zepdrix

And no, it doesn't matter which order you write them in. If you had written -3x -5x in that order, we would end up with the same result. So don't worry about that.

26. zepdrix

Yes. And please please please try to get in the habit of putting a plus sign between the groups. Very annoying mistake that a lot of students make lol

27. zepdrix

(5x^2-5x) + (-3x+3) k good :) now factor it out

28. anonymous

Oh, sorry! So I got 5(x^2 - x) + 3(-x +1)

29. zepdrix

MOAR :O moar stuff

30. anonymous

What do you mean?

31. zepdrix

$\large\rm 5(\color{orangered}{x^2 - x}) + 3(-x +1)$Well, there is more in this orange stuff. The two terms in orange still share something in common. Taking the 5 out was good, but there is moar.

32. anonymous

Oh! Okay so it's 5x(x-1) + 3(-x+1)

33. zepdrix

Mmmm k good.$\large\rm 5x(\color{orangered}{x-1}) + 3(\color{orangered}{-x +1})$But how do we get these orange parts to match up? Hmm maybe we forgot to pull something out the second set of brackets?

34. anonymous

5x(x-1) + -3(x+1) lol (:

35. zepdrix

$\large\rm \left[5x\color{orangered}{(x-1)}-3\color{orangered}{(x-1)}\right]$OK good :O We factored the two brackets completely. I artificially placed some square brackets. We now want to pull anything similar from both terms out of the square brackets.

36. zepdrix

Hint Hint, I color-coded the thing we're pulling out :3

37. anonymous

Lol so we just get 5x-3 (:

38. zepdrix

$\large\rm \left[5x\color{orangered}{(x-1)}-3\color{orangered}{(x-1)}\right]\quad=\quad\color{orangered}{(x-1)}\left[5x-3\right]$Well we can't forget about the factor we pulled out, ya? But yes, we end up with only 5x-3 in the square brackets.

39. zepdrix

You don't have to use square brackets if you don't want :P That was just help explain the process. So our final result from factoring is:$\large\rm 5x^2-8x+3\quad=\quad (x-1)(5x-3)$

40. zepdrix

Did the factoring from the square brackets step make sense? :o I know that one can be a little tricky.

41. anonymous

Ohhh my bad lol i just wasnt thinking, for some reason I thought the (x-1) just canceled out.. Lol so let me see if I can simplify now

42. anonymous

Yayyyy! I solved it (: I got 4/x-11 thank you bunches

43. zepdrix

yay \c:/