When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.
Similarly, we will factor the polynomials first:
[tex] x^4+3x^3 = x^3(x+3)[/tex]
[tex]x^2-9 = (x+3)(x-3)[/tex]
[tex]x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2[/tex]
The following factors emerged:
- [tex]x,\ x^3[/tex] We will choose [tex]x^3[/tex] because it has the higher exponent
- [tex]x-3[/tex]
- [tex]x+3,\ (x+3)^2[/tex] We will choose [tex](x+3)^2[/tex] because it has the higher exponent.
So, the LCM is
[tex]x^3(x-3)(x+3)^2[/tex]
