Algebra II

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Our current assignment is to find the LCM, Least Common Multiple of two polynomials. I think I'm doing it right but I'm not quite sure. For the first question:

2t^2+t-3, 2t^2+5t+3

I have 2t^2+t+3 as the LCM. Is this correct or can somebody step me through the correct method to complete the problem?

2t^2+t-3 = (2t+3)(t-1)
2t^2+5t+3 =(2t+3)(t+1)

Therefore (2t+3)(t-1)(t+1) is a multiple of both polynomials. It is also the Least Common Multiple

(2t+3)(t-1)(t+1) can be written as
(2t+3)(t^2-1)= 2t^3 +3t^2 -2t -3

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