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Factorising quadratics

Discussion in 'Mathematics' started by lancsHOD, Mar 27, 2011.

  1. lancsHOD

    lancsHOD New commenter

    How do you teach factorising a quadratic when the coefficient of x squared isn't one? I can think of at least three different methods and just wondered which way you teach it?
  2. pipipi

    pipipi New commenter

    In that case I multiply first by last, then look at factors of that product that combine to sum of 'middle' coefficient. the middle coefficent then gets separated into those two factors and the four subsequent terms get factorised in first pair and then second pair.
    hope that method makes sense by the time I've mashed it up.

    It would be good to know some other methods (unless you mean the quadratic formula)
  3. bombaysapphire

    bombaysapphire Star commenter

    I have in the past used the method of splitting the x-coefficient but in recent years my groups haven't seemed to like it. I now show it as an option later on but none of my students appear to have adopted it recently.
    I make sure I have taught FOIL to expand double brackets and then get students to write:
    F,OI, L above the three terms.
    Starting with a prime co-efficient of x squared then they can decide on the first terms and come up with the options for the last. They can then see which give the right result for the OI in the middle.
    It seems to be an area where students need lots and lots of regular practice.
  4. Nazard

    Nazard New commenter

    This is one reason I like the box method for multiplication so much.
    Once they are used to using the boxes to expand quadratics we then use them for factorising. They know that the ax^2 part goes in the top left box and the numerical part goes in the bottom right. They then try things to see what works.
    This is very similar to bombaysapphire's method, but using boxes instead of FOIL.
    [I do like the idea of being able to write "oi!" on a maths question, though!]
  5. Basic inspection

    Hope that in an exam situation at least one of a or c is prime as otherwise it can be time consuming

    In truth ... just look at the possibilities
  6. Set them one - let them have a go at it. Get them to describe their methods.
    Set a couple more - one which plays to their favourite method, one which is problematic for it.

    Does that count as a method?
  7. I think trial and improvement works best, but it needs regular practice and hence is not usually popular with students. I just happened to try factorising 6x^2 + 5x ? 6 when I read this and out of the many possible combinations, I hit on the right combination first time by sheer luck. However, had I needed to solve 6x^2 + 5x ? 6 = 0 I would go straight for the quadratic formula as has been mentioned.
  8. As an aside, here are a couple of factorisation questions I found in a 1951 maths O level paper: 4x^2 -15ax-4a^2 and axy+2aby-xz-2bz. Possible A* questions perhaps.
  9. lancsHOD

    lancsHOD New commenter

    The three methods I was thinking of were;
    1. As you describe
    2. By inspection
    3. A lengthy way a colleague showed me that will always give you the factors...... can I explain it!
    I'll try, to factorise 2x<font face="Calibri">2</font>-9x+10
    Multiply coeff of x<font face="Calibri">2 </font>constant term, in this case 20.
    Find the factors of 20 that add to -9
    then write (2x-4)(2x-5) all divided by 2
    factorise the brackets were possible, 2(x-2)(2x-5) all divided by 2
    so answer is (x-2)(2x-5).
    Hope this makes sense, difficult to explain maths on computer!
  10. strawbs

    strawbs Established commenter

    snap!! although at school myself I was taught inspection.
  11. Sorry but this is a particularly easy example is it not?
  12. I also teach this method - although there's more writing for it, my students always get to the answer whereas other methods can be frustrating and students quite often give up.
  13. Not sure how many people here read the MA journal 'Maths in Schools' but there was an article about this in the September issue... I've scanned it in case it is of interest to others...
    There are some good things in both this and the ATM journal!

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