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Which of the following is a factor of both x^2-x-6 and x^2-5x +6? A. x-3 B. x+3 C. x-2...

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patriciabmcca... | High School Teacher | eNoter

Posted April 10, 2013 at 1:48 PM via web

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Which of the following is a factor of both x^2-x-6 and x^2-5x +6?

A. x-3

B. x+3

C. x-2

D x+2

 

 

2 Answers | Add Yours

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 10, 2013 at 1:57 PM (Answer #1)

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The common factor of the given expressions has to be determined.

x^2-x-6

= x^2 - 3x + 2x - 6

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

= (x + 2)(x - 3)

x^2 -5x +6

= x^2 - 3x - 2x + 6

= x(x - 3) - 2(x - 3)

= (x - 2)(x - 3)

The common factor is (x - 3)

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oldnick | Valedictorian

Posted April 11, 2013 at 2:42 AM (Answer #2)

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we have to find common solution of equations

`x^2 -5x+6`  and `x^2 - x - 6`

`x^2 - 5x+6=x^2 -3x -2x +6`  so :

`=x(x-3) -2(x-3)=(x-2)(x-3)`

On the other side: `x^2-x-6=x^2 - 3x + 2x -6`  

`=x(x-3)+2(x-3)=(x+2)(x-3)` 

so the common factor is   `x-3`

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