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Math Help - How to teach factoring

  1. #1
    MHF Contributor Amer's Avatar
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    How to teach factoring

    How i can teach my students how to factor numbers and variables
    I teach them the distributive law
    and the master it I tried to tell them that factoring is the anti of distributive law
    any ideas
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  2. #2
    Super Member Quacky's Avatar
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    Re: How to teach factoring

    My teacher just said it like this:

    Take the example of:
    x^2+6x+9
    Now, 6 is the "target number"

    We need to split 9 into it's factors,
    1,9 and 3,3
    and try to find a combination that will make 6. This is 3,3, so the factors are (x+3)(x+3)

    The next example he explained were of the type x^2-bx+c, ie. x^2-5x+4 because these factored into things of the form (x-a)(x-d) so they were easy to get our head around. Now, 5 is our target number and we look at the factors of 4:
    4,1
    2,2 and we can get the target number with 4, 1 so the factors are (x-4)(x-1)

    Then came x^2-ax-b, ie x^2-2x-8. Again, 2 is our "target number" and again we look at the factors of 8 which are 1,8 and 4,2
    clearly 4-2=2 so the factors are (x\pm  2)(x\mp  4) and then we could just adjust the signs as necessary to get -2.

    Etc, etc.
    When it came to things of the form ax^2+bx+c, it would be the same thing, except this time you'd have to use both the factors of a and the factors of c to get the target number.

    For cubics, quartics, etc, which we didn't cover until 2 years later, we just learned the factor, remainder and rational roots theorems, which made things very straightforward.
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  3. #3
    MHF Contributor Amer's Avatar
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    Re: How to teach factoring

    not that what i mean
    I mean something like this 2x^2 - 4x = 2x(x-2)
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  4. #4
    Super Member Quacky's Avatar
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    Re: How to teach factoring

    Then, consider this approach:

    Split 2x^2 into its factors:
    2\times{x}\times{x}

    Split 4x into its factors:
    2\times 2\times x

    Now look for factors which are common to both, which here are 2\times x and isolate these:
    2x[\cdots]

    Then, just list the remaining factors.
    2x(x-2)

    Another example, 6x^2-3x

    6x^2=3\times 2\times x\times x
    3x=3\times{x}

    Common are 3\times{x}

    =3x[\cdots]

    Then, filling in the remaining factors:

    =3x(2x-1)
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  5. #5
    MHF Contributor Amer's Avatar
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    Re: How to teach factoring

    nice idea I will try it, I think giving much examples will make it good for them
    Thanks
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  6. #6
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    Re: How to teach factoring

    sort of a tangent, but one way i have always thought of polynomials with integer coefficients, is "integers in base x". that is, we use the same rules in multiplying, adding, subtracting and dividing, that we do with ordinary integers, it's just that base x is so big, we never get from the "1's" place to the "x's" place or from the "x's" place to the "x^2's" place.

    the distributive law is....well, you just cannot stress enough how important it is. it splits AND collects, it slices, it dices, it's a whole kitchen in one!
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  7. #7
    MHF Contributor Amer's Avatar
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    Re: How to teach factoring

    since I am new in teaching field so I always try to learn from others how to teach
    I think I was suppose that my students should learn from one example which is not true
    I found out that giving examples for the way or the techniques of something with different ways they will learn it without trying to teach them the basic things
    Thanks
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