1.

(b) Find the HCF of `51x^(2) (x + 3)^(3) (x -2)^(2) and 34 x(x -1)^(5) (x -2)^(3)`

Answer» Let `f(x) = 51 x^(2) (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 . x^(2) (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) = 17 x (x -2)^(2)`


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