The highest common factor (HCF) of x2 - 1,x4 - 1 and x4 - x3 + x - 1 is
Solution
Correct Answer: Option C
প্রশ্নে বলা হয়েছে, (x² - 1), (x⁴ - 1) এবং (x⁴ - x³ + x - 1) এর গ.সা.গু. কত?
১ম রাশি,
(x² - 1)
= x² - 1²
= (x + 1)(x - 1)
২য় রাশি,
(x⁴ - 1)
= (x²)² - 1²
= (x² + 1)(x² - 1)
= (x² + 1)(x + 1)(x - 1)
৩য় রাশি,
(x⁴ - x³ + x - 1)
= x³(x - 1) + 1(x - 1)
= (x - 1)(x³ + 1)
= (x - 1)(x + 1)(x² - x + 1)
১ম রাশি,
(x² - 1)
= x² - 1²
= (x + 1)(x - 1)
২য় রাশি,
(x⁴ - 1)
= (x²)² - 1²
= (x² + 1)(x² - 1)
= (x² + 1)(x + 1)(x - 1)
৩য় রাশি,
(x⁴ - x³ + x - 1)
= x³(x - 1) + 1(x - 1)
= (x - 1)(x³ + 1)
= (x - 1)(x + 1)(x² - x + 1)
অতএব, গ.সা.গু. হল: (x - 1)(x + 1) = x² - 1
উত্তর: x² - 1
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