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

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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)**

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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