# How do you divide (2x^3-11x^2+13x-44)div(x-5) using synthetic division?

Mar 8, 2018

$2 {x}^{2} - 1 x + 8 \textcolor{w h i t e}{\text{xxx}} \frac{- 4}{x - 5}$

#### Explanation:

Note:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{m a \ge n t a}{5}$ (used below) is the value of $x$ required to make the divisor, $\left(x - 5\right)$ equal to zero.

rows [0] and [4] are not really part of synthetic division; I include them for reference purposes only.

row [1] are the coefficients of the powers of $x$ (when the expression is formed in standard notation and using $0$ for any missing powers of $x$).

row [2] contains, for each column, the product of $\textcolor{m a \ge n t a}{5}$ (see above) and the value from the previous column of row [3].

row [3] contains, for each column, the sum of the values in the same column for rows [1] and [2]

The notations used in the (optional) row 4 are the powers of $x$ from the (optional) row [1] reduced by 1, with the final column, marked as $\textcolor{g r a y}{\text{R}}$, the remainder.

{: ([0],," | ",color(gray)(x^3),color(white)("x")color(gray)(x^2),color(white)("x")color(gray)(x^1),color(white)("x")color(gray)(x^0)), ([1],," | ",2,-11,+13,-44), ([2],ul(+color(white)("xx"))," | ",ul(color(white)("xxxx")),ul(color(white)("x")10),ul(color(white)("x")-5),ul(color(white)("x")40)), ([3],xx color(magenta)5," | ",color(white)("x")2,color(white)("x")-1,color(white)("xxx")8,color(white)("x")-4), ([4],," | ",color(gray)(x^2),color(white)("x")color(gray)(x^1),color(white)("xx")color(gray)(x^0),color(white)("xx")color(gray)R) :}

Normally when performing synthetic division, only rows [1], [2], and [3] are required.