Question

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

Answer 1

According to factor theorem if y-1 is a factor of y^20 - 1 and y^21 - 1 then it's zero y(1)= 0.

=) 1^20 - 1
=) 1 - 1
=) 0.
And
=) 1^21 - 1
=) 1 - 1
=) 0.

Hence y-1 is a factor of y^20 -1 and y^21 -1.

Hope it's helpful to u.

Answer 2

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 !