Question: Find the H.C.F. of p(x) = 2x3 - 3x2 - 2x + 3 and q(x) = 3x2 + 8x + 5.

Solution:
Given that,
p(x) = 2x3 - 3x2 - 2x + 3 and q(x) = 3x2 + 8x + 5

Now,
The factors of p(x) = 2x3 - 3x2 - 2x + 3
⇒ x2(2x - 3) - 1(2x - 3)
⇒ (x2 - 1)(2x - 3)
⇒ (x + 1)(x - 1)(2x - 3)

And,
The factors of q(x) = 3x2 + 8x + 5
⇒ 3x2 + 5x + 3x + 5
⇒ x(3x + 5) + 1(3x + 5)
⇒ (3x + 5)(x + 1)

∴ The required H.C.F. is (x + 1).