The HCF of (x 3 - y 2 - 2x) and (x 3 + x 2) is

Let f(x) = x³ - y² - 2x = x( x² - x- 2)
= x( x² - 2x + x - 2)
= x {x (x - 2) + 1 (x -2)}
= x (x +1) (x - 2)
and g(x) = x³ + x²
= x² (x +1) = x. x (x +1)
∴ LCM of [ f(x), g(x)] = x (x +1) . x . (x - 2)
= x²(x + 1)(x - 2)
= x²(x² - x - 2)
= x⁴ - x³ - 2x²