# How do you divide (4x^3 -12x^2+5x+3)/((x +3) )?

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Feb 9, 2018

$4 {x}^{2} - 24 x + 77 , R - 228$

#### Explanation:

polynomial long division - yay!

Then teach the underlying concepts
Don't copy without citing sources
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#### Explanation

Explain in detail...

#### Explanation:

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Jim G. Share
Feb 10, 2018

$4 {x}^{2} - 24 x + 77 - \frac{228}{x + 3}$

#### Explanation:

$\text{one way is to use the divisor as a factor in the numerator}$

$\text{consider the numerator}$

$\textcolor{red}{4 {x}^{2}} \left(x + 3\right) \textcolor{m a \ge n t a}{- 12 {x}^{2}} - 12 {x}^{2} + 5 x + 3$

$= \textcolor{red}{4 {x}^{2}} \left(x + 3\right) \textcolor{red}{- 24 x} \left(x + 3\right) \textcolor{m a \ge n t a}{+ 72 x} + 5 x + 3$

$= \textcolor{red}{4 {x}^{2}} \left(x + 3\right) \textcolor{red}{- 24 x} \left(x + 3\right) \textcolor{red}{+ 77} \left(x + 3\right) \textcolor{m a \ge n t a}{- 231} + 3$

$= \textcolor{red}{4 {x}^{2}} \left(x + 3\right) \textcolor{red}{- 24 x} \left(x + 3\right) \textcolor{red}{+ 77} \left(x + 3\right) - 228$

$\text{quotient "=color(red)(4x^2-24x+77)," remainder } = - 228$

$\Rightarrow \frac{4 {x}^{3} - 12 {x}^{2} + 5 x + 3}{x + 3}$

$= 4 {x}^{2} - 24 x + 77 - \frac{228}{x + 3}$

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