The greatest common divisor of f(x) = x³ − 12x² + 47x − 60 and g(x) = x² − 5x + 6, will bef(x) = x³ − 12x² + 47x − 60 और g(x) = x² − 5x + 6 का महत्तम समापवर्तक होगा

Explanation

g(x) = (x − 2)(x − 3). f(2) = 8 − 48 + 94 − 60 = −6 ≠ 0 but f(3) = 27 − 108 + 141 − 60 = 0, so in fact f(x) = (x − 3)(x − 4)(x − 5). The only common factor is x − 3.g(x) = (x − 2)(x − 3)। f(2) = 8 − 48 + 94 − 60 = −6 ≠ 0 परन्तु f(3) = 27 − 108 + 141 − 60 = 0, वस्तुतः f(x) = (x − 3)(x − 4)(x − 5)। अतः उभयनिष्ठ गुणनखण्ड केवल x − 3 है।