If x - 9 is a factor of x² - 5x - 36, what is the other factor?

Solution:

Given polynomial x² - 5x - 36

To factorize the polynomial x² – 5x – 36, we will split the middle term that is the coefficient of 'x'.

⇒ x² + 4x - 9x – 36

⇒ x (x + 4) - 9 (x + 4)

⇒ (x + 4) (x - 9)

Hence, the factors that satisfy the polynomial x² – 5x – 36 are (x + 4) and (x - 9).

Thus the other factor is (x + 4)

If x - 9 is a factor of x² - 5x - 36, what is the other factor?

Summary:

If x - 9 is a factor of x² - 5x - 36, then the other factor is (x + 4).