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Trinomials watch

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    How do I factor trinomials for example 9x^2-6x+1
    • TSR Community Team

    TSR Community Team
    (Original post by Mr T's Student)
    How do I factor trinomials for example 9x^2-6x+1
    Heya, I'm going to put this in the Maths forum for you as you should get more responses there.

    You should also check out the forum to see if there's any other threads there which might be helpful to you! http://www.thestudentroom.co.uk/forumdisplay.php?f=38

    (Original post by Mr T's Student)
    How do I factor trinomials for example 9x^2-6x+1
    1. First check whether this is a complete square of sum of two terms
    2 if this isn' t, then check whether the factor of quadratic term is not equal 1
    IIf this is not, then take out this factor . and continue the completing in the brackets goto 3.
    3. complete the first 2 terms to square by adding and subtracting
    the proper third term
    3. THe subtracted third term bring out from the brackets (multiplying by factor before brackets if it is needed) and add to the original term remainded out of brackets and substitute this
    with the square of the square root of tt.
    4. So you have two squares. If there is minus sign between them then
    you can factorize this with the rule of
    \displaystyle A^2-B^2=(A-B)(A+B)

    For the question: the point 1 is true

    9x^2 - 6x +1

    Take the square root of the quadratic (1st) term -> 3x
    Divide by 2 the 2nd term then divide by the root of 1st term ->-6x/2->-3x/3x ->-1
    Take on square this and if you get the third term this is a complete square -> (-1)^2=+1

    - square of the difference of 3x and 1 because

    \displaystyle \left (a-b\right )^2=a^2-2ab+b^2
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Updated: June 12, 2014

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