If HCF of x 3 - 10m 2 + 31x - 30m and x 2 - 8mx + 15 is a linear polynomial, then what is the value of m?

Go through options. Put m = 1 in two given expression,we have x³ - 10x² + 31x - 30 and x² - 8x + 15 x² - 8x + 15 = (x - 5) (x - 3) x³ - 10x² + 31x - 30 = (x - 2) (x - 5) (x - 3) ∴ (x - 5) (x - 3) = x² - 8x + 15 is the HCF of both expressions. ∴ m = 1