Question

Determine o mmc dos seguintes polinômios

a) 6x e 9x
b) 5x elevado a 2 e 10x
c) x elevado a 3 e x elevado a 2
d) 5x e 7y
e) 3xy e xy elevado a 2
f) 4a elevado a 2 b e 2a elevado a 3
g) 3x elevado a 2 e 9x elevado a 3y elevado a2
h) 6x elevado a 2 y e 24xz elevado a 4
i) 5x elevado a 2, 10xy elevado a 2 e 2x elevado a 3 z
j) 2x e x+3
k) 3x e 3x+9
l) x + 8 e x + 1

Answer 1

$m.m.c.\\ \\a)\\\\ 6x~~~9x~~|~3\\ 2x~~~3x~~|~2\\~~x~~~3x~~|~3\\ ~~x~~~~~x~~|~x\\ ~~1~~~~~1~~~~~~~~~~~~~~~m.m.c.=3.2.3.x=18x$

$b)\\ \\ 5x^{2} ~e~10x~~~~~~(5x^{2} =5.x.x)\\ \\ 5xx~~~~10x~|~2\\ 5xx~~~~~5x~|~5\\ ~~xx~~~~~~~x~|~x\\ ~~~~x~~~~~~~1~|~x\\ ~~~~1~~~~~~~~~~~~~~~~~~~~~~~m.m.c.=2.5.x.x=10x^{2}$

$c)\\ \\ x^{3}~e~x^{2} ~~(x.x.x~~e~~x.x)\\ \\ xxx~~~~xx~|x\\ ~~xx~~~~~~x~|~x\\ ~~~x~~~~~~~1~|~x\\ ~~~1~~~~~~~~~~~~~~~~~~~~m.m.c.=x.x.x=x^{3}$

$d)\\ \\ 5x~~e~~7y\\ \\ 5x~~~~7y~|5x\\ ~~~1~~~7y~|~7y\\ ~~~~~~~~~~1~~~~~~~~~~~~m.m.c.=(5x).(7y)=35xy$

$e)\\ \\ 3xy~~e~~xy^{2} ~~~~~~~(xy^{2} =x.y.y)\\ \\ 3xy~~~~xyy~|~3\\ ~~xy~~~~xyy~|~x\\ ~~~~y~~~~~~yy~|~y\\ ~~~~1~~~~~~~y~|~y\\ ~~~~~~~~~~~~~1~~~~~~~~~~~~m.m.c.=3.x.y.y=3xy^{2}$

$f)\\ \\ 4a^{2} ~~~~b~~~~2a^{3} ~|2\\ 2a^{2} ~~~~b~~~~~a^{3} ~|~2\\ ~~~a^{2} ~~~~b~~~~a^{3} ~|~a^{2} \\ ~~~1~~~~~b~~~~~a~~|~b\\ ~~~~~~~~~1~~~~~~a~|~a\\ ~~~~~~~~~~~~~~~~1~~~~~~~~~~~~m.m.c.=2.2.a^{2} .a.b=4a^{3} b$

$g)\\ \\ 3x^{2} ~,~9x^{3} ~e~y^{2} \\ \\ 3x^{2} ~~9x^{3} ~~y^{2} ~|~3\\ ~~x^{2} ~~3x^{3} ~~y^{2} ~|~3\\ ~~x^{2} ~~~x^{3} ~~~y^{2} ~|~x^{2} \\ ~~1~~~~~x~~~~y^{2} ~|~x\\ ~~~~~~~~1~~~~y^{2} ~|~y^{2} \\ ~~~~~~~~~~~~~~~1~~~~~~~~~~~~m.m.c=3.3.x^{2} .x.y^{2} =9x^{3} y^{2}$

$h)\\ \\ 6x^{2} ~~~~y~~~~24xz^{4} ~|~6\\ ~~x^{2} ~~~~y~~~~~~4xz^{4} ~|~4\\ ~~x^{2} ~~~~y~~~~~~~xz^{4} ~|~x\\ ~~x~~~~~y~~~~~~~~~z^{4} ~|~x\\ ~~1~~~~~~y~~~~~~~~z^{4} ~|~y\\ ~~1~~~~~~1~~~~~~~~z^{4} ~|~z^{4} \\ ~~~~~~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~m.m.c.=6.4.x.x.y.z^{4} =24x^{2} yz^{4}$

$i)\\ \\ 5x^{2} ~~10xy^{2} ~~2x^{3} z~|~2\\ 5x^{2} ~~~~5xy^{2} ~~~x^{3}z ~|~5\\ ~~ x^{2} ~~~~~~xy^{2} ~~~x^{3}z~|~x\\ ~~x~~~~~~~~y^{2} ~~~~x^{2} z~|~x\\ ~~1~~~~~~~~y^{2} ~~~~~xz~|~x\\ ~~~~~~~~~~~~y^{2} ~~~~~~z~|~y^{2} \\ ~~~~~~~~~~~~1~~~~~~~~z~|~z\\~~~~~~~~~~~~~~~~~~~~~1 ~~~~~~~~m.m.c.=2.5.x.x.x.y^{2} .z=10x^{3} y^{2} z$

$j)\\ \\ 2x~e~(x+3)~~~m.m.c=2x(x+3)=2x^{2} +6x$

$k)\\ \\ 3x~e~3x+9~~~m.m.c=3x(3x+9)=9x^{2} +27x$

$l)\\ \\ x+8~e~x+1~~~~m.m.c.=(x+8)(x+1)=x^{2} +x+8x+8=\\ \\ x^{2} +9x+8$