Find the H.C.F. of p(x) = x³ - 9x and q(x) = x² + 2x - 15.

Question: Find the H.C.F. of p(x) = x³ - 9x and q(x) = x² + 2x - 15.

Solution:
Given that, p(x) = x³ - 9x and q(x) = x² + 2x - 15

Now, the factors of p(x) = x³ - 9x
⇒ x(x² - 9)
⇒ x(x + 3)(x - 3)

And, the factors of q(x) = x² + 2x - 15
⇒ x² + 5x - 3x - 15
⇒ x(x + 5) - 3(x + 5)
⇒ (x - 3)(x + 5)

∴ The required H.C.F. is (x - 3)