Question

IF L.C.M. and H.C.F. of two expressions are $\left(x^2+6x+8\right)\left(x+1\right)$ and $\left(x+1\right)$ respectively and one equation is $x^2+3x+2$ then what will be the other equation?

• A. $x^2+5x+4$
• B. $x^2-5x+4$
• C. $x^2+4x+5$
• D. $x^2-4x+5$

Answer 1

The correct option is A $x^2+5x+4$

Given $H.C.F,L.C.M$ of two expressions as $(x+1)(x^2+6x+8),(x+1)$.Let the expressions be $a,b$.

If $a,b$ are two numbers and their $H.C.F,L.C.M$ are $c,d$ then we know that $a\times b=c\times d$.

Using this we can conclude that ;

$a\times b=(x+1{)}^2(x^2+6x+8)$

given one of the $a,b$ is $(x^2+3x+2)=(x+1)(x+2)$

$(x+1{)}^2(x^2+3x+2)=(x+1{)}^2(x+2)(x+4)$

$=\left[\right(x+1\left)\right(x+2\left)\right(x+1\left)\right]\left[\right(x+4\left)\right]$

$=[x^2+3x+2][x^2+5x+4]$

hence the other expression is $x^2+5x+4$