Question

How do you find the remainder for `(2x^2+x-6)div(x+2)`?

Answer 1

`(2x^2+x-6)=(x+2)(2x-3)+(0)`

`"Remainder"=0`

Explanation:

Using synthetic division :

`diamond(2x^2+x-6)div(x+2)`

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

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

`-2 |` `2color(white)(.......)1color(white)(..)-6`
`ulcolor(white)(....)|` `ul(0color(white)( ...)-4color(white)(.......)6`
`color(white)(......)2color(white)(...)-3color(white)(.......)color(violet)(ul|0|`
We can see that , quotient polynomial :

`q(x)=2x-3 and"the Remainder"=0`

Hence ,

`(2x^2+x-6)=(x+2)(2x-3)+(0)`
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