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Product of Two Numbers = HCF X LCM of the Two Numbers

Find the HCF ...

Question

Find the HCF of $(x^{2} - 4) (x^{2} - x - 2)$ and $(x^{2} + 4 x + 4) (x^{2} - 3 x + 2)$

x^{2} - 4

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{(x + 2)}^{2}

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{(x - 2)}^{2}

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x^{2} - 1

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Solution

The correct option is A $x^{2} - 4$
Prime factorisation of $(x^{2} - 4) (x^{2} - x - 2) = [(x + 2) \times (x - 2)] \times [(x - 2) \times (x + 1)] = (x + 2) \times {(x - 2)}^{2} \times (x + 1)$
Prime factorisation of $(x^{2} + 4 x + 4) (x^{2} - 3 x + 2) = [(x + 2) \times (x + 2)] \times [(x - 2) \times (x - 1)] = (x - 2) \times {(x + 2)}^{2} \times (x - 1)$
So,HCF $= (x + 2) \times (x - 2) = (x^{2} - 4)$

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