Question

How do you divide `(2x^3+3x^2-8x+3)div(x+3)`?

Answer 1

`(2x^3+3x^2-8x+3)/(x+3)=2x^2-3x+1`

Explanation:

So

`(2x^3+3x^2-8x+3)/(x+3)=2x^2-3x+1`

Answer 2

`2x^2-3x+1`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(2x^2)(x+3)color(magenta)(-6x^2)+3x^2-8x+3`

`=color(red)(2x^2)(x+3)color(red)(-3x)(x+3)color(magenta)(+9x)-8x+3`

`=color(red)(2x^2)(x+3)color(red)(-3x)(x+3)color(red)(+1)(x+3)color(magenta)(-3)+3`

`=color(red)(2x^2)(x+3)color(red)(-3x)(x+3)color(red)(+1)(x+3)+0`

`rArr(2x^3+3x^2-8x+3)/(x+3)`

`=(cancel((x+3))(2x^2-3x+1))/(cancel((x+3))`

`=2x^2-3x+1`