Find the LCM of the given polynomial. 3x^{2}-27, 2x^{2}-x-15

zakinutuzi 2021-12-13 Answered
Find the LCM of the given polynomial.
3x227,2x2x15
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Expert Answer

Robert Pina
Answered 2021-12-14 Author has 42 answers
Step 1
The lowest common multiple of 2 polynomials can be obtained factorizing both the polynomials. The factors that are common are taken only once in the product term of the lowest common multiple.
The factors that are not common are then multiplied with the common factors to obtain the lowest common multiple. The lowest common multiple of polynomials is also a polynomial.
Step 2
The polynomial 3x227 is factorized as follows:-
3x227=3(x29)
=3(x+3)(x-3)
The polynomial 2x2x15 is factorized as follows:-
2x2x15=2x26x+5x15
=2x(x-3)+5(x-3)
=(2x+5)(x-3)
Step 3
The common factor between the 2 polynomials is (x−3). The other factors are obtained as 3, (x+3) and (2x+5). Thus the lowest common multiple is the product of these factors and obtained as follows:-
LCM=3(x-3)(x+3)(2x+5)
=3(x29)(2x+5)
=(3x227)(2x+5)
=6x3+15x254x135
Thus the lowest common multiple of 3x227 and 2x2x15 is obtained to be 6x3+15x254x135.

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ambarakaq8
Answered 2021-12-15 Author has 31 answers

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