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Find L.C.M and H.C.F. of the following expression x2 + 6x + 9, x2 – x – 12, x3 + 4x2 + 4x + 3

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Expression x2 + 6x + 9 

= (x)2 + 2 × x × 3 + (3)2

x3 + 4x2 + 4x + 3 = (x + 3)(x2 + x + 1) …(iii)

common  factor of eqn. (i), (ii) and (iii) = (x + 3)

Thus, required H.C.F. = (x + 3)

in eqns. (i), (ii) (iii)

= (x + 3)2 (x – 4) (x2 + x + 1)

= (x2 + 6x + 9) (x3 – x2 + x – 4x2 – 4x – 4)

Hence, required L.C.M 

= (x2 + 6x + 9) (x3 – 5x2 – 3x – 4)

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