Question

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

Answer 1

Answer:

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

Answer 2

For y-1 to be a factor of y^20 - 1 and y^21-1, remainder must be zero.

Using remainder theorem

Let p(y) = p(1)    [because y-1 = 0 thus y=1]

p(1) = 1^20-1 = 1-1 = 0

q(y) = 1^21-1 = 1-1 = 0

Thus, y-1 is factor of both p(y) and q(y)