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Find the HCF and LCM of 51x^2 (x+3)^3 (x-2) ^2 & 34x (x-1) ^5 (x-2) |
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Answer» Let f(x) = 51x²(x + 3)³(x − 2)² and g(x) = 34(x − 1)5(x − 2)³ Writing f(x) and g(x) as the product of the POWERS of irredcible factors f(x) = 17. 3. x²(x + 3)³. (x − 2)² = g(x) 17.2. x(x - 1)5. (x − 2)³ = The common factors with the least exponents are 17, x and (x - 2)² ... The HCF of the given polynomials = 17. x. (x - 2)² = 17X(x − 2)² Writing f(x) and g(x) as the product of powers of irreducible factors f(x) = 17.3x²(x + 3)³. (x - 2)² g(x) = 17. 2(x - 1)³. (x − 2)³ Now all the factors (TAKEN only once) with the highest expoinents are 2, 3, 17, x²(x − 1)5, (x − 2)³ and (x+3)³ ... The LCM of the given polynomials = 2.3.7. x²(x - 1)³. (x - 2)³ . (x+3)³ = 102x²(x - 2)³(x - 1)³(x +3)³ |
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