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Factors,how do they work?

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Well,i never paid attention to maths,few things i learned and now i need to solve calculus(dont ask why) but to do that i need to first understand how factoring works,its a basic thing,yes ,i'v missed it and can't go on without it.
    2. Relevant equations
    Few examples and solutions from the book.
    1) x^3-3x^2=x^2(x-3)
    2) x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)
    3) 4x^2-1=(2x-1)(2x+1)
    4) x^3-x=x(x^2-1)=x(x-1)(x+1)

    3. The attempt at a solution
    I spent few hours to understand them by myself but couldn't.
    Can anyone explain in details how exactly this works?
    Help the newb.
     
  2. jcsd
  3. Mar 12, 2010 #2
    x^3 = x multiplied by x multiplied by x
    similarly x^2 is equal to x multiplied by x

    so [tex]x^{3} - 3 x^{2} = x. x. x - 3. x. x[/tex]

    Take out what is common in between. Here common term is x.x
    so x. x can be written as [tex]x^2[/tex]

    so it is equal to [tex]x^{2}(x-3)[/tex]

    And for all the rest, you have to know one formula

    [tex](x^{2} - a^{2}) = (x - a)(x + a)[/tex]

    Actually the your problem is so easy that it is difficult for me to tell. And I think that's the reason why nobody has answered it yet. I don't know how to explain such problems but I've tried my best.
     
    Last edited: Mar 12, 2010
  4. Mar 12, 2010 #3
    Before you can think of factoring the expression of the left, you should know
    how to multiply the factored expression on the right, to get the expression
    on the left.
     
  5. Mar 12, 2010 #4

    Mark44

    Staff: Mentor

    If you're studying calculus now, and are mystified by factoring, you've really got your work cut out for you. Realistically, you will probably need to spend half or more of your time brushing up on algebra and trig concepts in order just to be able to understand the work shown in examples. And that doesn't include being able to work the problems through from start to finish.

    Some people can do this, and some can't, and this depends to a fair degree on their motivation or lack thereof. Unlike some other disciplines, success at one level of mathematics requires a solid understanding of the preceding subjects. You might be able to understand some of the calculus concepts at a high level, but if you can't factor expressions or do the other things that you are expected to have mastered, it's going to be very difficult.
     
  6. Mar 12, 2010 #5
    I'm telling you my way of studying Maths. I never try to understand by looking at the examples. I start solving it, doesn't matter whether i know it or not. and when you'll stuck look at book to know how they had cleared that bump
     
  7. Mar 12, 2010 #6

    Char. Limit

    User Avatar
    Gold Member

    The reason why [tex]x^2-a^2=(x+a)(x-a)[/tex] is this:

    Let's expand [tex](x+a)(x-a)[/tex]

    [tex](x+a)x-(x+a)a[/tex]

    [tex]x^2+ax-ax-a^2[/tex]

    [tex]x^2-a^2[/tex]

    Apply similar ideas to the rest.
     
  8. Mar 13, 2010 #7
    Am failure of digits ,a beggar of numbers ,am a dying equation ;(

    Ok now,why maths are separated in to pre and post calculus?
    I just need to learn algebra first right?
     
  9. Mar 13, 2010 #8

    Mark44

    Staff: Mentor

    Yes, and trigonometry as well. As I said before, in order to succeed in calculus, you first have to have the foundations in place.
     
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