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

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

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Answer 1 · 2017-07-21T19:23:46

$\frac{3 v^{3} + 12 v^{2} + 10 v - 6}{v + 2} = 3 u^{2} + 6 u - 2 - \frac{2}{v + 2}$ $(3v^3+12v^2+10v-6)/(v+2)=3u^2+6u-2-2/(v+2)$

Explanation:

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So :

$(3 v^{3} + 12 v^{2} + 10 v - 6) = (3 v^{2} + 6 v - 2) (v + 2) - 2$ $(3v^3+12v^2+10v-6)=(3v^2+6v-2)(v+2)-2$

Answer 2 · 2017-07-21T20:10:16

$3 v^{2} + 6 v - 2 - \frac{2}{v + 2}$ $3v^2+6v-2-2/(v+2)$

Explanation:

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

$consider the numerator$ $"consider the numerator"$

$3 v^{2} (v + 2) - 6 v^{2} + 12 v^{2} + 10 v - 6$ $color(red)(3v^2)(v+2)color(magenta)(-6v^2)+12v^2+10v-6$

$= 3 v^{2} (v + 2) + 6 v (v + 2) - 12 v + 10 v - 6$ $=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(magenta)(-12v)+10v-6$

$= 3 v^{2} (v + 2) + 6 v (v + 2) - 2 (v + 2) + 4 - 6$ $=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(red)(-2)(v+2)color(magenta)(+4)-6$

$= 3 v^{2} (v + 2) + 6 v (v + 2) - 2 (v + 2) - 2$ $=color(red)(3v^2)(v+2)color(red)(+6v)(v+2)color(red)(-2)(v+2)-2$

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

$\Rightarrow \frac{3 v^{3} + 12 v^{2} + 10 v - 6}{v + 2}$ $rArr(3v^3+12v^2+10v-6)/(v+2)$

$= 3 v^{2} + 6 v - 2 - \frac{2}{v + 2}$ $=3v^2+6v-2-2/(v+2)$

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

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