Final answer:
To find the LCM of the given polynomials 2x+3x²-x+1-2x²+8x³, we need to factor each polynomial and then find the product of their highest powers. The highest power of x in the polynomial is x³. Therefore, the LCM of the given polynomials is x³.
Step-by-step explanation:
To find the LCM of the given polynomials 2x+3x²-x+1-2x²+8x³, we need to factor each polynomial and then find the product of their highest powers.
The given polynomial can be factored as x(3x-1)+1-(2x²-8x³).
The highest power of x in the polynomial is x³. Therefore, the LCM of the given polynomials is x³.