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Question
Show that m − 1 is a factor of m21 − 1 and m22 − 1.
Solution
Let p(m) = m21 − 1 and q(m) = m22 − 1.
Divisor = m − 1
Now,
p(1) = (1)21 − 1
= 1 − 1
= 0
Therefore, by factor theorem (m − 1) is a factor of p(m) = m21 − 1.
Also,
q(1) = (1)22 − 1
= 1 − 1
= 0
Therefore, by factor theorem (m − 1) is a factor of q(m) = m22 − 1.
Hence, (m − 1) is a factor of m21 − 1 and m22 − 1.
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