# How do find the quotient of (2x^3 − 3x 2 + x − 6) ÷ (x − 4)?

## How do find the quotient of (2x^3 − 3x^2 + x − 6) ÷ (x − 4)?

Aug 11, 2018

The quotient polynomial :
$q \left(x\right) = 2 {x}^{2} + 5 x + 21 \mathmr{and} \text{the Remainder} = 78$

#### Explanation:

$\left(2 {x}^{3} - 3 {x}^{2} + x - 6\right) \div \left(x - 4\right)$

Using synthetic division :

We have , $p \left(x\right) = \left(2 {x}^{3} - 3 {x}^{2} + x - 6\right) \mathmr{and} \text{divisor : } x = 4$

We take ,coefficients of $p \left(x\right) \to 2 , - 3 , 1 , - 6$

. $4 |$ $2 \textcolor{w h i t e}{\ldots .} - 3 \textcolor{w h i t e}{\ldots \ldots .} 1 \textcolor{w h i t e}{\ldots \ldots .} - 6$
$\underline{\textcolor{w h i t e}{\ldots}} |$ ul(0color(white)( .........)8color(white)(.......)20color(white)(.........)84
color(white)(....)2color(white)(........)5color(white)(.......)21color(white)(......)color(violet)(ul|78|
We can see that , quotient polynomial :

$q \left(x\right) = 2 {x}^{2} + 5 x + 21 \mathmr{and} \text{the Remainder} = 78$

Hence ,

$\left(2 {x}^{3} - 3 {x}^{2} + x - 6\right) = \left(x - 4\right) \left(2 {x}^{2} + 5 x + 21\right) + \left(78\right)$