1.

Find the L.C.M of 2(x3 + x2 – x – 1) and 3(x3 + 3x2 – x – 3)

Answer»

2[x3 + x2 – x – 1] = 2[x2(x + 1) - 1 (x + 1)]

= 2(x + 1) (x2 – 1)

= 2(x + 1) (x + 1) (x – 1)

= 2(x + 1)2 (x – 1)

3[x3 + 3x2 – x – 3] = 3[x2(x + 3) - 1 (x + 3)]

= 3[(x + 3)(x2 – 1)]

= 3(x + 3)(x + 1) (x – 1)

L.C.M. = 6(x + 1)2 (x – 1) (x + 3)



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