Show that m – 1 is a factor of m21 – 1 and m22 – 1.

1.	Show that m – 1 is a factor of m21 – 1 and m22 – 1.
Answer» i. p(m) = m – 1 Divisor = m – 1 ∴ take m = 1 Remainder = p(1) p(m) = m²¹ – 1 ∴ P(1) = 1²¹ – 1 = 1 – 1 = 0 ∴ By factor theorem, m - 1 is a factor of m²¹ -1. ii. p(m) = m²² – 1 Divisor = m – 1 ∴ take m = 1 Remainder = p(1) p(m) = m²² – 1 ∴ P(1) = 1²² – 1 = 1 – 1 = 0 ∴ By factor theorem, m -1 is a factor of m²² – 1.

Answer»

i. p(m) = m – 1

Divisor = m – 1

∴ take m = 1

Remainder = p(1)

p(m) = m²¹ – 1

∴ P(1) = 1²¹ – 1 = 1 – 1 = 0

∴ By factor theorem, m - 1 is a factor of m²¹ -1.

ii. p(m) = m²² – 1

Divisor = m – 1

∴ take m = 1

Remainder = p(1)

p(m) = m²² – 1

∴ P(1) = 1²² – 1 = 1 – 1 = 0

∴ By factor theorem, m -1 is a factor of m²² – 1.

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