Question

prove that x-1 is the factor of both x^99-1 and x^100-1

Answer 1

If x - 1 is a factor, then x= 1 should satisfy the equations.

1) x^99 - 1 = 0

Put x  = 1 

1 -1 = 0

So, it is a factor

2) x^100 - 1

Put x = 1

1-1 = 0

So, it is a factor

Answer 2

TAKE LIKE
P(X) = X^99-1
P(Y) = X^100-1

ACCORDING TO THE FACTOR THEREOM IF X-1 IS THE FACTOR OF P(X) AND P(Y) THEN THEN P(1) = 0

P(X) = X^99-1
P(1) = (1)^99-1
P(1) = 1-1
P(1) = 0


SO P(1) BECOME ZERO SO X-1 IS THE FACTOR OF P(X)


P(Y) = X^100-1
P(1) = (1)^100-1
P(1) = 1-1
P(1) = 0

SO P(1) BECOME ZERO SO X-1 IS THE FACTOR OF P(Y)