Question

Show that y-1 is a factor of y^20 -1 and y^21 -1

Answer 1

Hey there , 

We know that ( x-a) is a factor of f(x) then f(a)=0 .

so ,

Here f(y) = y^20-1 

g(y ) = y²¹-1 

If ( y -1) is a factor of f(y) then f(1) =0

f(1) 

= 1^20-1

=0

Hence ( y -1) is a factor of y^20-1 

===============-------------==============

If ( y -1) is a factor of g(y) then g(1) =0

g(1) 

= 1^21-1

=0

Hence ( y -1) is a factor of y^21 -1 

Therefore, ( y-1 ) is a factor of y^20 -1 and y^21 -1 


Hope it helped !

Answer 2

If it is y-1 then y = 1
= Y^20- 1 = 1^20 -1 = 0
= Y^21 -1 = 1^21-1 = 0