Find the least common multiple of the following pair of polynomials:x(x-1)^2(x+1) and 4(x-1)(x+1)^3

Emily-Jane Bray

Emily-Jane Bray

Answered question

2021-09-03

Find the least common multiple of the following pair of polynomials:
x(x1)2(x+1) and 4(x1)(x+1)3

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-09-04Added 91 answers

The least common multiple (LCM) is the smallest quantity which is multiple of more than one quantity. To find the LCM of two polynomials, we have to perform the following process.
Factors each polynomial
Take out the common factors of both polynomials
Multiply the remaining uncommon factors
Multiply the common and uncommon factors to each other to find the LCM.
The given polynomials already have the factors. So take the common factors of polynomials x(x1)2(x+1) and 4(x1)(x+1)3. The common factors are x-1 and x+1.
The remaining uncommon factors are x(x-1) and 4(x+1)2. The product of these factors is 4x(x1)(x+1)2. Now, multiply 4x(x1)(x+1)2 with common factors to obtain the LCM of both polynomials
LCM=4x(x1)(x+1)2(x1)(x+1)
=4x(x1)2(x+1)3
Hence, the least common multiple of the given polynomials is 4x(x1)2(x+1)3.

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