Let the HCF and LCM of f(x)and g(x)be H and L. If H, L and F(x) are given, then can g(x)be determined uniquely. please justify the answer.

Asked by praju99 | 9th Jul, 2011, 02:28: AM

Expert Answer:

It is known that the product of two polynomials is equal to the product of their HCF and LCM.
Here, the two polynomials are f(x) and g(x), HCF = H and LCM = L
 
So, f(x).g(x) = H.L
This gives
g(x) = H.L/ f(x)
 
Thus, the polynomial g(x) can be determined uniquely by the above formula.

Answered by  | 8th Jul, 2011, 10:03: PM

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