Question

LCM and HCF of $(x+1{)}^2$ and $x^3+1$

• A. HCF = $(x-1)$ LCM = $(x+1)(x^2-x+1)$
• B. HCF = $(x+1)$ LCM = $(x+1)(x^2-x-1)$
• C. HCF = $(x+11)$ LCM = $(x+1)(x^2-5x+1)$
• D. HCF = $(x+1)$ LCM = $(x+1{)}^2(x^2-x+1)$

Answer 1

The correct option is D

HCF = $(x+1)$

LCM = $(x+1{)}^2(x^2-x+1)$

First expression $(x+1{)}^2=(x+1\left)\right(x+1)$

Second expression $x^3+1=(x+1)(x^2-x+1)$

HCF = $(x+1)$

LCM = $(x+1{)}^2(x^2-x+1)$