If HCF of x3 - 10m2 + 31x - 30m and x2

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If HCF of x³ - 10m² + 31x - 30m and x² - 8mx + 15 is a linear polynomial, then what is the value of m ?

1. 2
2. 3
3. 1
4. 4

Correct Option: C

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