# Which of the following is a factor of both x^{2 }- x - 6 and x^{2 }- 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.

x^{2 }- x - 6

By splitting up the middle term

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

Taking out the common terms

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

= (x + 2)(x - 3)

x^{2 }- 5x + 6

By splitting up the middle term

= x^{2} - 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).

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

**Summary:**

The factor of both x^{2 }- x - 6 and x^{2 }- 5x + 6 is (x - 3).