How do you divide $\frac{12 x^{3} + 2 + 11 x + 20 x^{2}}{2 x + 1}$ $(12x^3+2+11x+20x^2) / (2x+1)$ ?

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How do you divide $\frac{12 x^{3} + 2 + 11 x + 20 x^{2}}{2 x + 1}$ $(12x^3+2+11x+20x^2) / (2x+1)$ ?

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Answer 1 · 2016-04-23T12:03:44

$6 x^{2} + 7 x + 2$ $6x^2+7x+2$

Explanation:

Rearrange the top expression to standard format

$\frac{12 x^{3} + 20 x^{2} + 11 x + 2}{2 x + 1}$ $(12x^3+20x^2+11x+2)/(2x+1)$

I prefer to set the question as long division. How many $2 x$ $2x$ s can you take from $12 x^{3} ? \frac{12}{2} = 6, \frac{x^{3}}{x} = x^{2} .$ $12x^3? 12/2 = 6, x^3/x = x^2.$ So, $6 x^{2}$ $6x^2$

Multiply the divisor $2 x + 1$ $2x+1$ by $6 x^{2}$ $6x^2$ and subtract.
$(2 x + 1) \times (6 x^{2}) = (12 x^{3} + 6 x^{2})$ $(2x+1)xx(6x^2)=(12x^3+6x^2)$
$(12 x^{3} + 20 x^{2} + 11 x + 2) - (12 x^{3} + 6 x^{2}) = (14 x^{2} + 11 x + 2)$ $(12x^3+20x^2+11x+2)-(12x^3+6x^2)=(14x^2+11x+2)$

How many $2 x$ $2x$ s can you take from $14 x^{2}$ $14x^2$ ? ..... $7 x$ $7x$

Multiply the divisor $2 x + 1$ $2x+1$ by $7 x$ $7x$ and subtract.
$(14 x^{2} + 11 x + 2) - (14 x^{2} + 7 x) = (4 x + 2)$ $(14x^2+11x+2)-(14x^2+7x)=(4x+2)$

How many $2 x$ $2x$ s can you take from $4 x$ $4x$ ?.....2

Multiply the divisor $2 x + 1$ $2x+1$ by $2$ $2$ and subtract.
$(4 x + 2) - (4 x + 2) = 0$ $(4x+2)-(4x+2) = 0$

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How do you divide $\frac{12 x^{3} + 2 + 11 x + 20 x^{2}}{2 x + 1}$ $(12x^3+2+11x+20x^2) / (2x+1)$ ?

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How do you divide (12x^3+2+11x+20x^2) / (2x+1)12x3+2+11x+20x22x+1(12x^3+2+11x+20x^2) / (2x+1)?

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How do you divide $\frac{12 x^{3} + 2 + 11 x + 20 x^{2}}{2 x + 1}$ $(12x^3+2+11x+20x^2) / (2x+1)$ ?