(11) Show that m – 1 is a factor of m21 – 1 and m22 – 1.
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Answer:
Yes (m-1) is a factor of m21 - 1 and m22 -1
Step-by-step explanation:
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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