Answer :
First, we can factor out a 4 from both polynomials to simplify the calculation:
4( x³ - 4x² + 5x - 2 ) and 8( x³ - 6x² + 9x - 4 )
Next, we can find the prime factorization of each polynomial:
4( x - 1 )( x - 1 )( x - 2 ) and 8( x - 2 )( x - 2 )( x - 1 )
The LCM is the product of the highest powers of each prime factor, so:
LCM = 4 * 2 * ( x - 1 ) * ( x - 2 ) * ( x - 2 ) = 8( x - 1 )( x - 2 )²
4( x³ - 4x² + 5x - 2 ) and 8( x³ - 6x² + 9x - 4 )
Next, we can find the prime factorization of each polynomial:
4( x - 1 )( x - 1 )( x - 2 ) and 8( x - 2 )( x - 2 )( x - 1 )
The LCM is the product of the highest powers of each prime factor, so:
LCM = 4 * 2 * ( x - 1 ) * ( x - 2 ) * ( x - 2 ) = 8( x - 1 )( x - 2 )²
