Question

Assertion (A): If (x - 1) is a common factor of f(x) and g(x), then f(1) = g(1).
Reason (R) : The common factor of f(x) and g(x) is their HCF.​

Answer 1

Step-by-step explanation:

1) If (x - 1) is a common factor of f(x) and g(x), then

f(1) = g(1).

By factor theorem

If (x-1) is a factor then by factor theorem f(1)=0---(1)

and similarly , g(1)=0----(2)

since x-1 is a common factor of f(x) and g(x)

=>f(1)=g(1)

2) The common factor of f(x) and g(x) is their HCF.

Let (x-a) is a factor of f(x) then

f(x)=(x-a)q1(x).....(1)

and g(x)=(x-a)q2(x)---(2)

From (1)&(2)

Common factor (x-a)

it is the heighest Common factor

so HCF=x-a