Question

prove that (x-1) is a factor of both x^99-1 and x^100-1

Answer 1

(x-1)= 0 therefore x = 1 

=x^99-1
=1^91-1
=1-1
=0

and

=x^100-1
=1^100-1
=1-1
=0 

so , it is proved that (x-1) is a factor of these two .

Answer 2

GIven: Here we have given $(x-1)$ and   $x^{99}-1$ and $x^{100}-1$

To find: Here we have to prove that (x-1) is a factor of both $x^{99}-1$ and $x^{100}-1$

Solution:

Here we have given $(x-1)= 0$  

therefore $x = 1$

$=x^{99}-1\\=1^{99}-1\\=1-1\\=0$

we will do the same in the second equation

$=x^{100}-1\\=1^{100}-1\\=1-1\\=0$

Here we have proved that (x-1) is a factor of these two equation

Final answer:

Hence (x-1) is a factor of these two equation