f(x)= (x-2)^54 is divided by x-1

Question

I neeeeed help!! please and thank you!

 

Answer 1

f(x) = (x-2)^54

From the remainders theorem if p(x)/(x-a) = q(x) with r(x)

p(x) = (x-a)q(x)+r(x)

Here the divisior is x-1

f(1) = (1-2)^54

= (-1)^54

= 1

x-1 divides(x-2)^54 then the remander is 1.