How do you find the LCM of #2z^5+4z^4-6z^3# and #3z^8+18z^7+27z^6#?

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Answer 1 · 2017-09-13T05:32:03

LCM is #6z^9+30z^8+18z^7-54z^6#

We have

#2z^5+4z^4-6z^3=2z^3(z^2+2z-3)=2z^3(z+3)(z-1)# and

#3z^8+18z^7+27z^6=3z^6(z^2+6z+9)=3z^6(z+3)^2#

Common factors are #z^3(z+3)#

other remaing factors in the two polynomials are #2(z-1)# and #3z^3(z+3)#

Hence LCM is #z^3(z+3)xx2(z-1)xx3z^3(z+3)#

= #6z^6(z+3)^2(z-1)#

= #6z^6(z^3+5z^2+3z-9)#

= #6z^9+30z^8+18z^7-54z^6#