Question

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)`?

Answer 1

The quotient polynomial :
`q(x)=2x^2+5x+21 and"the Remainder"=78`

Explanation:

`(2x^3-3x^2+x-6)div(x-4)`

Using synthetic division :

We have , `p(x)=(2x^3-3x^2+x-6) and "divisor : " x=4`

We take ,coefficients of `p(x) to 2,-3,1,-6`

. `4 |` `2color(white)(....)-3color(white)(.......)1color(white)(.......)-6`
`ulcolor(white)(...)|` `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(x)=2x^2+5x+21 and"the Remainder"=78`

Hence ,

`(2x^3-3x^2+x-6)=(x-4)(2x^2+5x+21 )+(78)`