Factorise : `x^2+2sqrt2 x-6` x^2+2√2 x-6

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Factorize  `x^2+2sqrt2 x-6`

First consider the factors of `x^2` and 6 which will enable you to arrive at a middle term of `2sqrt2 x` . We can use the factors of `x^2` as `x times x` .

The standard factors for 6 (ie `1 times 6` or `3 times 2` ) will not work. However, knowing that `sqrt2 times sqrt 2 = 2` means that we can use `3sqrt2 times sqrt2` as our factors because they equal 6:

`3sqrt2 times sqrt2= 3 times (sqrt2)^2=3 times 2 = 6`

And to arrive at a middle term of `2sqrt2x` , we multiply `x times 3sqrt2=3sqrt2 x` and `x times sqrt2=sqrt2 x` and minus the` sqrt2 x ` from `3sqrt2 x` :

`3sqrt2 x-sqrt2x=2sqrt2x` which is what we need.  


`therefore x^2 +2sqrt2 x-6`

`= (x-sqrt2)(x+3sqrt2)`

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ajju | College Teacher | (Level 1) Adjunct Educator

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i factorize x^2+2√2 x-6 by quadratic formula: