The H.C.F. and L.C.M. of two expressions are $(x - 3)$ and $(x^{3} - 5 x^{2} - 2 x + 24)$ respectively. If one of the expression is $(x^{2} - 7 x + 12)$ , find the other.

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Solution

Given
$H = x - 3$
$L = x^{3} - 5 x^{2} - 2 x + 24$
$A = x^{2} - 7 x + 12$
$B = ?$
$B = \frac{H \times L}{A}$
$B = \frac{(x - 3) \times (x^{3} - 5 x^{2} - 2 x + 24)}{(x^{2} - 7 x + 12)}$
$∴$ $B = (x - 3) (x + 2)$
$B = x^{2} - x - 6$

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The H.C.F. and L.C.M. of two expression are (x − 3) and (x³ − 5x² − 2x + 24) respectively. If one of the expression is (x² − 7x + 12) find the other.

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