Which of the following is a factor of both x2- x-6 and x2 - 5x + 6
To find a factor that is common to both polynomials, we can use the method of factoring.
First, let's factor the polynomials:
x^2 - x - 6
(x - 3)(x + 2)
x^2 - 5x + 6
(x - 2)(x - 3)
From the factored forms, we can see that (x - 3) is a common factor to both polynomials.
x^2-x-6 = (x-3)(x+2)
x^2-5x+6 = (x-3)(x-2)
we can substract one term from the other and solve for x
(x^2-5x+6)-(x^2-x-6)=0
-4x+12=0
-4x=-12
x=-12/-4
x=3
therefore, (x-3) is a factor of both polynomials