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Method of factorising quadratics when coefficient is greater than 1? Watch

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    Hey, I was just wondering if there is an easy method of factorising quadratics when the coefficient is greater than 1. For example, 1 question is 6x^2-11x-7=0. In school, we are just taught to do it in our heads but on questions like this it gets hard so I want to know a written method of solving this sort of questions

    Thanks.
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    AC= 6*-7= -42
    something that multiplys to get -42 but adds to get -11
    = -14 +3 = -11
    =-14 x 3 =-42
    new equation = 6x^2-14x+3x-7
    (6x^2-14x)+(3x-7)
    factorise (both brackets must be equal)
    (6x^2-14x)+(3x-7)
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    2x(3x-7) + (3x-7)
    (3x-7) (2x+1) ?
    not sure if its plus one in last bracket though
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    You can always plug the numbers into the quadratic solution to get the roots directly, then back out the brackets that way.

    E.g.

    x = 7/3 and -1/2, from the general quadratic equation solution

    so the factors must be (3x - 7) and (2x + 1)

    i.e. when these factors are zero, x equals the answers we calculated.
 
 
 
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