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When m12 - 1 is divided by m + 1, the remainder is:
Answer & Solution
Correct Answer:
Option
C
m12 - 1
= (m6)2 - (1)2
= (m6 + 1)(m6 - 1)
= (m6 + 1){(m3)2 - (1)2}
= (m6 + 1)(m3 - 1)(m3 + 1)
= (m6 + 1)(m3 - 1)(m + 1)(m2 + m + 1)
Hence m + 1 is factor of m12 - 1.
It will completely divide it and give remainder 0.
= (m6)2 - (1)2
= (m6 + 1)(m6 - 1)
= (m6 + 1){(m3)2 - (1)2}
= (m6 + 1)(m3 - 1)(m3 + 1)
= (m6 + 1)(m3 - 1)(m + 1)(m2 + m + 1)
Hence m + 1 is factor of m12 - 1.
It will completely divide it and give remainder 0.
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