Question

If the $LCM$ and $HCF$ of two expressions are $(x^2+6x+8)$ $(x+1)$ and $(x+1)$ respectively and one of the expression is $x^2+3x+2,$ then find the other.

• 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 $x^2+5x+4$

L.C.M $\Rightarrow (x^2+6x+8)(x+1)$

$\Rightarrow (x^2+4x+2x+8)(x+1)$

L.C.M $\Rightarrow (x+4)(x+2)(x+1)$

H.C.F $\Rightarrow (x+1)$

concept :

$\Rightarrow L.C.M\times H:C.F$ = first Expression $\times$ second Expression

$(x+4)(x+2)(x+2{)}^2=(x^2+3x+2\left)\right(b)$

$=(x^2+2x+x+2)\left(b\right)$

$(x+4)(x+2)(x+1{)}^2=(x+2\left)\right(x+1\left)\right(b)$

b = (x + 4)(x + 1)

$=x^2+4x+x+4$

$b=x^2+5x+4$