InterviewSolution
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InterviewSolution
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(a) Find the HCF of `28x^(4)` and `70x^(6)`. (b) Find the HCF of `48x^(2) (x + 3)^(2) (2x-1)^(3) (x + 1)` and `60x^(3) (x+ 3) (2x-1)^(2) (x + 2)`. |
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Answer» (a) Find f(x) = `28x^(4)` and g(x) = `70 x^(6)`. Writing f(x) and g(x) as a product of powers of irreducible factors , we have f(x) = `2^(2) xx 7 xx x^(4)` and g(x) = `2 xx 5 xx 7 xx x^(6)`. `therefore` The common factors with the least exponents are 2 , 7 and `x^(4)`. `implies` HCF = `2 xx 7 xx x^(4) = 14 x^(4)` (b) Let f(x) = `48x^(2) (x + 3)^(2) (2x - 1)^(3) (x + 1)` and g(x) = `60 x^(3) (x + 3) (2x - 1)^(2) (x + 2)`. Writing f(x) and g(x) as the product of the powers of irreducible factors , we have f(x) = `2^(4) xx 3 xx x^(2) (x + 3)^(2) (2x - 1)^(3) (x + 1)` g (x) = `2^(2) xx 3 xx 5 xx x^(3) (x + 3) (2x - 1)^(2) (x + 2)`. The common factors with least exponents are `2^(2) , 3 , x^(2) , x + 3 ` and `(2x-1)^(2)`. `therefore` HCF = `2^(2) xx 3 xx x^(2) (x + 3) (2x - 1)^(2) = 12 x^(2) (x + 3) (2x -1)^(2)`. |
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