Question

If L.C.M and H.C.F of two expression 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 $x^2+5x+4$

$x^2+6x+8=x^2+4x+2x+8=x(x+4)+2(x+4)=(x+4)(x+2)$

$x^2+3x+2=x^2+2x+x+2=x(x+2)+1(x+2)=(x+2)(x+1)$

First equation $\times$ Second equation = LCM $\times$ HCF

$\Rightarrow$ $(x^2+3x+2)\times$ Second equation $=(x^2+6x+8)(x+1)\times (x+1)$

$\Rightarrow$ $(x+2)(x+1)\times$ Second equation $=(x+4)(x+2)(x+1)(x+1)$

$\Rightarrow$ Second equation $=\frac{(x+2)(x+4)(x+1)(x+1)}{(x+2)(x+1)}$

$\Rightarrow$ Second equation $=(x+4)(x+1)$

$\Rightarrow$ Second equation $=x^2+4x+x+4$

$\therefore$ Second equation $=x^2+5x+4$