Question

LCM of polynomials 18(x^4-x^3+x^2) & 24(x^6+x^3)

Answer 1

Dear student
$$\begin{gathered} 18({\mathrm{x}}^4-{\mathrm{x}}^3+{\mathrm{x}}^2)\mathrm{and}24({\mathrm{x}}^6+{\mathrm{x}}^3) \\ \mathrm{Now}18({\mathrm{x}}^4-{\mathrm{x}}^3+{\mathrm{x}}^2) \\ =2\times 3^2\times {\mathrm{x}}^2\left({\mathrm{x}}^2-\mathrm{x}+1\right) \\ \mathrm{and}24({\mathrm{x}}^6+{\mathrm{x}}^3)=3\times 2^3\times {\mathrm{x}}^3\left({\mathrm{x}}^3+1\right)=3\times 2^3\times {\mathrm{x}}^3(\mathrm{x}+1)\left({\mathrm{x}}^2+1-\mathrm{x}\right) \\ \mathrm{So},\mathrm{LCM}\hspace{0.17em}\left(18({\mathrm{x}}^4-{\mathrm{x}}^3+{\mathrm{x}}^2),24({\mathrm{x}}^6+{\mathrm{x}}^3)\right)=72{\mathrm{x}}^3\left({\mathrm{x}}^3+1\right) \end{gathered}$$
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