# How do you divide (x^3-8x+3)div(x+3) using synthetic division?

Aug 12, 2018

$\frac{{x}^{3} - 8 x + 3}{x + 3} = {x}^{2} - 3 x + 1$

#### Explanation:

$\frac{{x}^{3} - 8 x + 3}{x + 3}$

$= \frac{{x}^{2} \left(x + 3\right) - 3 {x}^{2} - 8 x + 3}{x + 3}$

$= \frac{{x}^{2} \cancel{\left(x + 3\right)} - 3 x \cancel{\left(x + 3\right)} + 1 \cancel{\left(x + 3\right)}}{\cancel{\left(x + 3\right)}}$

$= {x}^{2} - 3 x + 1$

Aug 12, 2018

$\left({x}^{3} - 8 x + 3\right) = \left(x + 3\right) \left({x}^{2} - 3 x + 1\right) + \left(0\right)$

#### Explanation:

$\left({x}^{3} - 8 x + 3\right) \div \left(x + 3\right)$

Using synthetic division :

We have , $p \left(x\right) = \left({x}^{3} + 0 {x}^{2} - 8 x + 3\right) \mathmr{and} \text{divisor : } x = - 3$

We take , coefficients of $p \left(x\right) \to 1 , 0 , - 8 , 3$

$- 3 |$ $1 \textcolor{w h i t e}{\ldots \ldots . .} 0 \textcolor{w h i t e}{\ldots \ldots} - 8 \textcolor{w h i t e}{\ldots \ldots \ldots .} 3$
$\underline{\textcolor{w h i t e}{\ldots .}} |$ ul(0color(white)( ....)-3color(white)(..........)9color(white)(......)-3
color(white)(......)1color(white)(......)-3color(white)(........)1color(white)(..........)color(violet)(ul|0|
We can see that , quotient polynomial :

$q \left(x\right) = {x}^{2} - 3 x + 1 \mathmr{and} \text{the Remainder} = 0$

Hence ,

$\left({x}^{3} - 8 x + 3\right) = \left(x + 3\right) \left({x}^{2} - 3 x + 1\right) + \left(0\right)$