x > 2, then x2 – x – 6 i know that this factors into (x - 3)(x + 2) over (x - 2)(x+2) but where di

Algebra
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x > 2, then x2 – x – 6 i know that this factors into (x - 3)(x + 2)  over  (x - 2)(x+2) but where did the -x from the x2-x-6 go? i can understand why x2-6 would factor in to (x-3)(x+2) because theres 2 x's that get a spot in the factor. but it seems the -x has just disapired! 

Jul 17th, 2015

Thank you for the opportunity to help you with your question!

x^2-x-6  if you factorize

you first multiply -6*x^2=-6x^2

look for two factors when you multiply you get -6x^2 and when you add those two factors you get -x

the factors are -3x and 2x so this two factors will represent -x

x^2-3x+2x-6  here -x has been replaced by -3x and 2x

x^2-3x+2x-6

(x^2-3x)+(2x-6)

x(x-3)+2(x-3)

(x+2)(x-3)

 and when (x+2)(x-3)  is divided by  (x-2)(x+2)  

(x+2) will cancel in the numerator and denominator and the final answer will be 

(x-3)/(x-2)


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 17th, 2015

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