If the L.C.M. and H.C.F. of two expressions a | vedclass

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(A) We know that for any two expressions, the product of the expressions is equal to the product of their $H.C.F.$ and $L.C.M.$First expression $	ime

Vedclass · Accepted Answer

$x^{2}+5x+4$

Vedclass · Answer

(A) We know that for any two expressions, the product of the expressions is equal to the product of their $H.C.F.$ and $L.C.M.$First expression $	imes$ Second expression $= H.C.F. 	imes L.C.M.$Given:$L.C.M. = (x^{2}+6x+8)(x+1) = (x+2)(x+4)(x+1)$$H.C.F. = (x+1)$First expression $= x^{2}+3x+2 = (x+2)(x+1)$Let the second expression be $P(x)$.$(x+2)(x+1) 	imes P(x) = (x+2)(x+4)(x+1) 	imes (x+1)$$P(x) = \frac{(x+2)(x+4)(x+1)(x+1)}{(x+2)(x+1)}$$P(x) = (x+4)(x+1)$$P(x) = x^{2}+x+4x+4 = x^{2}+5x+4$

If the $L.C.M.$ and $H.C.F.$ of two expressions are $(x^{2}+6x+8)(x+1)$ and $(x+1)$ respectively, and one of the expressions is $x^{2}+3x+2$, find the other.

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