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2. Polynomials
medium
સાબિત કરો : $p-1$ એ $p^{10}-1$ અને $p^{11}-1$ નો એક અવયવ છે.
Option A
Option B
Option C
Option D
Solution
If $p-1$ is a factor of $p^{10}-1,$ then $(1)^{10}-1$ should be equal to zero.
Now, $(1)^{10}-1=1-1=0$
Therefore, $p-1$ is a factor of $p^{10}-1.$
Again, if $p -1$ is a factor of $p^{11}-1,$ then $(1)^{11}-1$ should be equal to zero. Now, $(1)^{11}-1=1-1=0.$
Therefore, $p -1$ is a factor of $p^{11}-1.$
Hence, $p -1$ is a factor of $p^{10}-1$ and also of $p^{11}-1.$
Standard 9
Mathematics
