Question

If the LCM of two polynomials is $(x-1{)}^2(x-2{)}^2$ and their HCF is $(x-1)(x-2)$, then the product of the polynomials is:

• A. $(x-1{)}^3(x-2{)}^3$
• B. $(x-1{)}^3(x-2{)}^2$
• C. $(x-1{)}^2(x-2{)}^3$
• D. $(x-1)(x-2)$

Answer 1

The correct option is A $(x-1{)}^3(x-2{)}^3$

LCM of two polynomials $\times$ HCF of two polynomials = Product of the polynomials.
$\Rightarrow (x-1{)}^2(x-2{)}^2\times (x-1)(x-2)=$ Product of the polynomials.

Hence, the product of the polynomials $=(x-1{)}^3(x-2{)}^3$