## Christos 2 years ago Factor this http://screencast.com/t/7oezPour5cV

1. ganeshie8

you dont knw how to factor

2. chocobo907

2x^2+x-3 factored would be (2x+3)(x-1)

3. ganeshie8

you have the answer there. @Christos something u dont understand in how to factor that ?

4. Christos

@ganeshie8 certainly I don't understand how I should start? Will you guys be willing to show me the first step? Thee are certain expressions that just dont ring a bell on me, it's not that I cant factor, just some specific ones

5. ganeshie8

i understand, let me guide u factor this

6. Christos

ty man

7. ganeshie8

$$2x^2 + x - 3$$

8. ganeshie8

compare it wid $$ax^2 + bx + c$$

9. Christos

ok

10. ganeshie8

we need to pick two numbers whose product equals $$ac$$, and sum equals $$b$$

11. ganeshie8

a=2 b=1 c=-3

12. ganeshie8

can you pick two numbers whose product equals -6, and sum equals 1 ?

13. surjithayer

$2x ^{2}+x-3=2x ^{2}+3x-2x-3$ (2*-3=-6,3-2=1) $=x \left( 2x+3 \right)-1\left( 2x+3 \right)=\left( 2x+3 \right)\left( x-1 \right)$

14. Christos

I dont think I can :(

15. ganeshie8

tell me what are the factors of -6

16. Christos

-1 -2 -3

17. ganeshie8

and 1, 2, 3 also

18. Christos

ooh ok

19. ganeshie8

so, 3 * -2 = -6

20. ganeshie8

3 + -2 = 1

21. ganeshie8

3 and -2 are our numbers !

22. Christos

So we dont take into considaration b ? We just add and multiply a and c?

23. ganeshie8

$$2x^2 + x - 3$$ you need to rewrite x as 3x-2x

24. ganeshie8

we did consider b, the numbers we pick must multiply to ac, and addup to b

25. Christos

"3 * -2 = -6" "3 + -2 = 1" Where is b ?

26. ganeshie8

we picked 3 and -2, cuz they multiply to ac, and addup to b

27. ganeshie8

look at the given expression, b = 1

28. Christos

hm the second expression ye

29. ganeshie8

$$2x^2 + x - 3$$ can be written as : $$2x^2 + 1x - 3$$

30. ganeshie8

compare it wid ax^2 + bx + c, and tell me whats b ?

31. Christos

yea I know it's 1, I just dont know what do it with it :D

32. Christos

lol

33. ganeshie8

so when you're asking where is b, you knw now that its there, and it is 1 :)

34. Christos

from my understanding we take a*c = whatever it gives then a+c = whatever it gives

35. ganeshie8

not exactly

36. Christos

hm

37. ganeshie8

we take a*c, tell whats a*c, in our current example ?

38. Christos

its -6

39. ganeshie8

so we take that -6, and find its factors. that addup to b

40. ganeshie8

-6 = 3*-2

41. Christos

when you say "add up" what do you mean exactly?

42. ganeshie8

when u add both the numbers, you must get b

43. ganeshie8

we picked 3 and -2, add them and see if u get b or not

44. ganeshie8

if p, q are the two numbers, you should pick them in a way such that :- pq = ac p+q = b

45. ganeshie8

thats all

46. Christos

I see now

47. ganeshie8

great :) you do few more problems u wil see more clearly

48. Christos

Ok so, we have a*c = -6 a-b = 1 but how do I proceed with this information in hand?

49. ganeshie8

heres the full solution, go through $$2x^2 + x - 3$$ $$2x^2 + 3x - 2x - 3$$ $$x(2x + 3) - 1(2x + 3)$$ $$(2x + 3)(x - 1)$$

50. Christos

a-c ***

51. ganeshie8

no

52. Christos

/facepalm I am such a dummy some times, I can see it clearly now, thanks again

53. ganeshie8

its, pq = ac p+q = b

54. ganeshie8

cool all geniuses have few dummy corners ;p

55. Christos

yea yea I see, I get you now

56. Christos

hihi xP

57. ganeshie8

good :)

58. Christos

ty dude