Two Polynomials H.C.F. (x-2) and L.C.M. (x3-5×2+6x). If one polynomial is (x2-2x) then find the second polynomial from the L.C.M. and H.C.F. relation method.

**Que: There are Two Polynomials Having H.C.F. (x-2) and L.C.M. (x3-5×2+6x). If one polynomial is (x2-2x) then find the second polynomial?**

**Solution: **In this question, we will use the relation formula of polynomials.

First of all, we will note down the available figures of the question:

H.C.F. of two polynomials = (x-2)

L.C.M. of the two polynomials = (x^{3}-5x^{2}+6x)

First polynomial is = (x^{2}-2x)

Second Polynomial =?

So, for finding out the second polynomial we will use standard formula of the polynomials.

**Product of polynomials = Product of H.C.F. and L.C.M.**

First Polynomial X Second Polynomial = L.C.M. X H.C.F.

Second Polynomial = (HCF * LCM)/(first polynomial)

Second Polynomial = [(x-2)(x^{3}-5x^{2}+6x)] / (x^{2}-2x)

=[(x-2)x(x^{2}-5x+6)] / x(x-2)

here we can see that x(x-2) is divisible

=(x^{2}-5x+6)

**So, the second polynomial is (x ^{2}-5x+6).**

## Two Polynomials H.C.F. (x-2) and L.C.M. (x3-5×2+6x). If one polynomial is (x2-2x) then find the second polynomial

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