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Find Least common multiple of
1-x^2 and (x-1)^3

User Marielle
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1 Answer

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Answer:

(x -1)³(x +1) = x⁴ -2x³ +2x -1

Explanation:

You want the least common multiple of (1 -x²) and (x -1)³.

LCM

The least common multiple (LCM) will be the product of the unique factors, each to its highest power.

1 -x² = -(x -1)(x +1)

(x -1)³ = (x -1)³

The unique factors to their highest powers are ...

(x -1)³ and (x +1)

The LCM is (x -1)³(x +1) = x⁴ -2x³ +2x -1.

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Additional comment

You may or may not want to add a minus sign in front of the LCM expression. We prefer to leave it with a positive leading coefficient. For whatever sign you choose, the leading coefficient of the quotients when divided by these expressions will have a minus sign on one or the other.

User Suraj Shingade
by
7.9k points

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