Question

If the LCM of two polynomials is $(x-3{)}^2(x-5{)}^3$ and their product is $(x-3{)}^2(x-5{)}^4$, then the HCF of the polynomials is:

• A. $(x-5)$
• B. $(x-3)$
• C. $(x-3{)}^4(x-5{)}^7$
• D. $(x-3)(x-5)$

Answer 1

The correct option is A $(x-5)$

LCM of two polynomials $\times$ HCF of two polynomials = Product of the polynomials.
$\Rightarrow (x-3{)}^2(x-5{)}^3\times HCF=(x-3{)}^2(x-5{)}^4$

Hence, the HCF of the polynomials $=\frac{(x-3{)}^2(x-5{)}^4}{(x-3{)}^2(x-5{)}^3}=(x-5)$.