Mathematics
The number of common factor(s) of two polynomials x2 - 9 and x3 - x2 - 9x + 9 is /are :
one
two
three
Factorisation
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Answer
Factorizing x2 - 9,
⇒ (x + 3)(x - 3)
Factorizing x3 - x2 - 9x + 9,
⇒ x2(x - 1) - 9(x - 1)
⇒ (x2 - 9)(x - 1)
⇒ (x + 3)(x - 3)(x - 1)
The number of common factor(s) of two polynomials x2 - 9 and x3 - x2 - 9x + 9 are two i.e.,(x + 3) and (x - 3).
Hence, Option 2 is the correct option.
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