Divide the following polynomial using synthetic division (x^3 + 6x^2 + 3x + 1 ) ÷ (x - 2)

Question

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&&\
\hline
&&&&\
&1&&&

\end{array}
$

ganeshie8 · Answer

multiply 1*2 and put it in next column

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&\
\hline
&&&&\
&1&&&

\end{array}
$

ganeshie8 · Answer

add 6 and 2,
put it down in last row

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&\
\hline
&&&&\
&1&8&&

\end{array}
$

ganeshie8 · Answer

multiply 2*8, 
put it in next column

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&16&\
\hline
&&&&\
&1&8&&

\end{array}
$

ganeshie8 · Answer

add 16 and 3,
put it down in last row

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&16&\
\hline
&&&&\
&1&8&19&

\end{array}
$

ganeshie8 · Answer

can u continue further ?

anonymous · Answer

shouldnt it be written something like x^2 + 5x etc...

ganeshie8 · Answer

yes, finish the synthetic division first

ganeshie8 · Answer

multiply 2*19,
and put it in next column

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&16&38\
\hline
&&&&\
&1&8&19&

\end{array}
$

ganeshie8 · Answer

add 38 and 1
and put it in the last row

ganeshie8 · Answer

$
\begin{array}{}

2~|&1&6&3&1\
&&2&16&38\
\hline
&&&&\
&1&8&19& | 39 \

\end{array}
$

ganeshie8 · Answer

so, 39 is the remainder

ganeshie8 · Answer

quotient can be written using the last row, leaving the remainder part

ganeshie8 · Answer

in the last row u have :

$1~~8~~19$

ganeshie8 · Answer

so the quotient is :

$x^2 + 8x + 19$

ganeshie8 · Answer

so,

$(x^3 + 6x^2 + 3x + 1 ) ÷ (x - 2) ~= ~ x^2 + 8x + 19 + \frac{39}{x-2}$

ganeshie8 · Answer

let me knw if smthng doesnt make sense...