Which of the following is a factor of both x² - x - 6 and x² - 5x + 6?
x - 3, x + 3, x - 2, x + 2 

Solution:

Let us find the factors of the quadratic polynomials using the splitting up of the middle term method.

x² - x - 6

By splitting up the middle term 

= x² - 3x + 2x - 6

Taking out the common terms

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

= (x + 2)(x - 3)

x² - 5x + 6

By splitting up the middle term

= x² - 3x - 2x + 6

Taking out the common terms 

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

= (x - 2)(x - 3)

Thus the common factor in both the polynomials is (x - 3)

Therefore, the common factor is (x - 3).

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Which of the following is a factor of both x² - x - 6 and x² - 5x + 6?

Summary:

The factor of both x² - x - 6 and x² - 5x + 6 is (x - 3).