How do you divide #\frac { 3v ^ { 3} + 12v ^ { 2} + 10v - 6} { v + 2}#?

2 Answers
Καδήρ Κ.
Jul 21, 2017

#(3v^3+12v^2+10v-6)/(v+2)=3u^2+6u-2-2/(v+2)#

Explanation:

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So :

#(3v^3+12v^2+10v-6)=(3v^2+6v-2)(v+2)-2#

Jim G.
Jul 21, 2017

#3v^2+6v-2-2/(v+2)#

Explanation:

#"one way is to use the divisor as a factor in the numerator"#

#"consider the numerator"#

#color(red)(3v^2)(v+2)color(magenta)(-6v^2)+12v^2+10v-6#

#=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(magenta)(-12v)+10v-6#

#=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(red)(-2)(v+2)color(magenta)(+4)-6#

#=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(red)(-2)(v+2)-2#

#"quotient "=color(red)(3v^2+6v-2)," remainder "=-2#

#rArr(3v^3+12v^2+10v-6)/(v+2)#

#=3v^2+6v-2-2/(v+2)#

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