Question

The HCF and LCM of two algebraic expressions respectively are (x-1) and $(x^2-1)$(x-1) If one of the expression is $(x^2-1)$ then the order is

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

Answer 1

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

The highest common factor of algebraic expression is known as H.C.F this is (x-1)

The lowest common multiple of algebraic expression is known as L.C.M this is $(x^2-1)(x-1)$

We know that equation =$L.C.M\times H.C.F$

So $(x^2-1)(x-1)\times (x-1)=(x^2-1)(x-1{)}^2$

If one of the expression is $(x^2-1)$

Then the other =$\frac{(x^2-1)(x-1{)}^2}{(x^2-1)}=(x-1{)}^2$