# How do you simplify and divide (b^3+8b^2-20b)div(b-2)?

Jun 27, 2018

${b}^{3} + 8 {b}^{2} - 20 b \div \textcolor{b l u e}{{b}^{2} + 10 b}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXX}}$with a remainder of $\textcolor{red}{0}$

#### Explanation:

Using synthetic division:
{: (,,color(gray)(b^3),color(gray)(b^2),color(gray)(b^1),color(gray)(b^0)), (," | ",1,+8,-20,color(white)("x")0), (+," | ",ul(" "),ul(color(white)("0")2),ul(color(white)("xx")20),ul(color(white)("x")0)), (xx 2," | ",1,10,color(white)("xx")0,color(white)("x")0), (,,color(gray)(b^2),color(gray)(b^1),color(white)("x")color(gray)(b^0),color(gray)("R")) :}

Jun 27, 2018

color(magenta)(b^2+10b

#### Explanation:

$\left({b}^{3} + 8 {b}^{2} - 20 b\right) \div \left(b - 2\right)$

$\textcolor{w h i t e}{\ldots} \textcolor{w h i t e}{\ldots \ldots .} {b}^{2} + 10 b$
$b - 2 | \overline{{b}^{3} + 8 {b}^{2} - 20 b}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \underline{{b}^{3} - 2 {b}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 10 {b}^{2} - 20 b$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{10 {b}^{2} - 20 b}$

color(magenta)(b^3+8b^2-20b-:b-2 = b^2+10b